Trắc nghiệm Bài tập ôn tập chương 1 Toán 8

<p><span style="font-size: medium;"> </span></p><div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 1 : </strong> </span><p><span style="font-size: medium;">Tích của đơn thức $x$ và đa thức $(1 – x)$ là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A. </span><span style="font-size: large;">\(1 - 2x\)</span></span> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B. </span><span style="font-size: large;">\(x - {x^2}\)</span></span> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C. </span><span style="font-size: large;">\({x^2} - x\)</span></span> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D. </span><span style="font-size: large;">\({x^2} + x\)</span></span> </li> </ul> <span style="font-size: medium;"><!--Câu 38954 loại 1.0--></span><div class="question c5bba31719104c05521d27fa7"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 2 : </strong> </span><p><span style="font-size: medium;">Tích của đa thức \(4{x^5} + 7{x^2}\) và đơn thức \(\left( { - 3{x^3}} \right)\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(12{x^8} + 21{x^5}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(12{x^8} + 21{x^6}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 12{x^8} + 21{x^5}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 12{x^8} - 21{x^5}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38956 loại 1.0--></span><div class="question c5bba320f9104c05521d27fad"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 3 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức \(A = \left( {{x^2} + 2 - 2x} \right)\left( {{x^2} + 2 + 2x} \right) - {x^4}\) ta được kết quả là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 4\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A =  - 4$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 19\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A =  - 19\)</span></p> </div> </li> </ul> </div> <span style="font-size: medium;"><ins class="982a9496" data-key="f20d92668a50143a6ac139eb35daaf25"></ins> <script async="" src="https://aj1559.online/ba298f04.js"></script> <!--Câu 38957 loại 1.0--></span><div class="question c5bba32509104c05521d27fb0"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 4 : </strong> </span><p><span style="font-size: medium;">Rút gọn đa thức \(16{x^2} - 4x + \dfrac{1}{4}\) ta được kết quả nào sau đây?</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {4x - \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {x - \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {4x + \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {x + \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38958 loại 1.0--></span><div class="question c5bba32959104c05521d27fb3"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 5 : </strong> </span><p><span style="font-size: medium;">Trong các khai triển hằng đẳng thức sau, khai triển nào sai?</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {A + B} \right)^2} = {A^2} + 2AB + {B^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {A - B} \right)^3} = {A^3} - 3{A^2}B - 3A{B^2} + {B^3}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({A^3} - {B^3} = \left( {A - B} \right)\left( {{A^2} + AB + {B^2}} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38959 loại 1.0--></span><div class="question c5bba32dc9104c05521d27fb6"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 6 : </strong> </span><p><span style="font-size: medium;">Cho biết \(3{y^2} - 3y\left( {y - 2} \right) = 36\). Giá trị của $y$ là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">5</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">6</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">7</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">8</span></p> </div> </li> </ul> </div> <span style="font-size: medium;"><ins class="982a9496" data-key="598f364461b0b6bfb2e7208ce4e46701"></ins> <script async="" src="https://aj1559.online/ba298f04.js"></script> <!--Câu 38960 loại 1.0--></span><div class="question c5bba33239104c05521d27fb9"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 7 : </strong> </span><p><span style="font-size: medium;">Giá trị của biểu thức \(A = 2x\left( {3x - 1} \right) - 6x\left( {x + 1} \right) - \left( {3 - 8x} \right)\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 16x - 3\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 3\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 16x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Đáp án khác</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38955 loại 1.0--></span><div class="question c5bba31c59104c05521d27faa"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 8 : </strong> </span><p><span style="font-size: medium;">Thực hiện phép tính \(\left( {{x^2} + x + 1} \right)\left( {{x^3} - {x^2} + 1} \right)\) ta được kết quả là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} + x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} - {x^4} + x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} + {x^4} + x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} - x - 1\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38961 loại 1.0--></span><div class="question c5bba337b9104c05521d27fbc"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 9 : </strong> </span><p><span style="font-size: medium;">Cho \(A = 5x\left( {4{x^2} - 2x + 1} \right) - 2x\left( {10{x^2} - 5x - 2} \right) - 9x + 1\). Chọn câu <strong>đúng.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 9x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 18x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 9x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Giá trị của biểu thức $A$ không phụ thuộc vào biến $x.$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38962 loại 1.0--></span><div class="question c5bba33b89104c05521d27fbf"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 10 : </strong> </span><p><span style="font-size: medium;">Tìm \(x\)  biết \(\left( {x + 2} \right)(x + 3) - \left( {x - 2} \right)\left( {x + 5} \right) = 6\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 5.\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 5.\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 10.\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 1.\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38963 loại 1.0--></span><div class="question c5bba33f39104c05521d27fc2"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 11 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức \({\left( {3x + 1} \right)^2} - 2\left( {3x + 1} \right)\left( {3x + 5} \right) + {\left( {3x + 5} \right)^2}\) ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(8\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(24\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38964 loại 1.0--></span><div class="question c5bba34369104c05521d27fc5"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 12 : </strong> </span><p><span style="font-size: medium;">Cho biết \({\left( {x + 4} \right)^2} - \left( {x - 1} \right)\left( {x + 1} \right) = 16\). Hỏi giá trị của \(x\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{1}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(8\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{1}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$ - 8\left( {x + 5} \right)$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38965 loại 1.0--></span><div class="question c5bba34749104c05521d27fc8"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 13 : </strong> </span><p><span style="font-size: medium;">Cho $x + y = 3$. Tính giá trị của biểu thức: $A = {x^2} + 2xy + {y^2} - 4x - 4y + 1$.</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{1}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$ - 2$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38966 loại 1.0--></span><div class="question c5bba34b89104c05521d27fcb"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 14 : </strong> </span><p><span style="font-size: medium;">Tìm \(x\) biết: \({\left( {x + 1} \right)^3} - {\left( {x - 1} \right)^3} - 6{\left( {x - 1} \right)^2} =  - 10\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - \dfrac{1}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 3$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38967 loại 1.0--></span><div class="question c5bba35009104c05521d27fce"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 15 : </strong> </span><p><span style="font-size: medium;">Kết quả phân tích đa thức \(6{x^2}y - 12x{y^2}\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x - 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x - y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x + 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x + y} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38968 loại 1.0--></span><div class="question c5bba35429104c05521d27fd1"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 16 : </strong> </span><p><span style="font-size: medium;">Điền đơn thức vào chỗ trống: \(12{x^3}{y^2}{z^2} - 18{x^2}{y^2}{z^4} = ....\left( {2x - 3{z^2}} \right)\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6x{y^2}{z^2}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6{x^2}{y^2}{z^2}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6{y^2}{z^2}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6{x^3}{y^2}{z^2}$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38969 loại 1.0--></span><div class="question c5bba35999104c05521d27fd4"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 17 : </strong> </span><p><span style="font-size: medium;">Tìm \(x\) biết: $2x\left( {x - 3} \right) + 5\left( {x - 3} \right) = 0$</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{5}{2}$ hoặc $x = 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x =  - \dfrac{5}{2}$ hoặc $x = 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{5}{2}$ hoặc $x =  - 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{2}{5}$ hoặc $x = 3$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38970 loại 1.0--></span><div class="question c5bba35e09104c05521d27fd7"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 18 : </strong> </span><p><span style="font-size: medium;">Tính giá trị của biểu thức $A = x\left( {x - 2009} \right) - y\left( {2009 - x} \right)$ tại $x = 3009$ và $y = 1991$:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$5000000$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$500000$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$50000$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$5000$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38971 loại 1.0--></span><div class="question c5bba362f9104c05521d27fda"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 19 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>sai.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(15{x^2} + 10xy = 5x\left( {3x + 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(35x\left( {y - 8} \right) - 14y\left( {8 - y} \right) = 7\left( {5x + 2y} \right)\left( {y - 8} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - x + 6{x^2}y - 12xy + 2 = \left( {6xy + 1} \right)\left( {x - 2} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^3} - {x^2} + x - 1 = \left( {{x^2} + 1} \right)\left( {x - 1} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38972 loại 1.0--></span><div class="question c5bba36749104c05521d27fdd"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 20 : </strong> </span><p><span style="font-size: medium;">Giá trị lớn nhất của \(x\)  thỏa mãn phương trình \(\;7{x^2}\left( {x - 7} \right) + 5x\left( {7 - x} \right) = 0\) là</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{5}{7}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 7$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 0$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 8$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38974 loại 1.0--></span><div class="question c5bba370b9104c05521d27fe3"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 21 : </strong> </span><p><span style="font-size: medium;">Đa thức \(12x - 9 - 4{x^2}\) được phân tích thành:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {2x - 3} \right)\left( {2x + 3} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - {\left( {2x - 3} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {3 - 2x} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - {\left( {2x + 3} \right)^2}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38976 loại 1.0--></span><div class="question c5bba37589104c05521d27fe9"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 22 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \({x^3} - 6{x^2}y + 12x{y^2} - 8{y^3}\) thành nhân tử:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {x - y} \right)^3}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${\left( {2x - y} \right)^3}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${x^3} - {\left( {2y} \right)^3}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${\left( {x - 2y} \right)^3}$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38983 loại 1.0--></span><div class="question c5bba393f9104c05521d27ffe"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 23 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức thành nhân tử: \(5{x^2} + 10xy - 4x - 8y\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {5x - 2y} \right)\left( {x + 4y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {5x + 4} \right)\left( {x - 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x + 2y} \right)\left( {5x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {5x - 4} \right)\left( {x - 2y} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38985 loại 1.0--></span><div class="question c5bba39c49104c05521d28004"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 24 : </strong> </span><p><span style="font-size: medium;">Điền vào chỗ trống: \(3{x^2} + 6x{y^2} - 3{y^2} + 6{x^2}y = 3\left( {...} \right)\left( {x + y} \right)\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><strong><span style="font-size: medium;">\(\left( {x + y + 2xy} \right)\)</span></strong></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - y + 2xy} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - y + xy} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - y + 3xy} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38991 loại 1.0--></span><div class="question c5bba3b899104c05521d28016"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 25 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \(m.{n^3} - 1 + m - {n^3}\) thành nhân tử, ta được:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {m - 1} \right)\left( {n + 1} \right)\left( {{n^2} - n + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({n^2}\left( {n + 1} \right)\left( {m - 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {m + 1} \right)\left( {{n^2} + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{n^3} - 1} \right)\left( {m - 1} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38992 loại 1.0--></span><div class="question c5bba3bf49104c05521d28019"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 26 : </strong> </span><p><span style="font-size: medium;">Điền vào chỗ trống \(4{x^2} + 4x - {y^2} + 1 = \left( {...} \right)\left( {2x + y + 1} \right)\):</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x + y + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x - y + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x - y\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x + y\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38999 loại 1.0--></span><div class="question c5bba3de89104c05521d2802e"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 27 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>đúng.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = {x^2}{\left( {x + 2} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = {x^2}{\left( {x - 2} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = {x^2}\left( {x - 2} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = x{\left( {x - 2} \right)^2}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38973 loại 1.0--></span><div class="question c5bba36c99104c05521d27fe0"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 28 : </strong> </span><p><span style="font-size: medium;">Có bao nhiêu giá trị của \(x\) thỏa mãn \({x^3} - 3{x^2} + 3 - x = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$1$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$2$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38977 loại 1.0--></span><div class="question c5bba37aa9104c05521d27fec"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 29 : </strong> </span><p><span style="font-size: medium;">Cho  \(4{x^2} - 25 - \left( {2x + 7} \right)\left( {5 - 2x} \right) = \left( {2x - 5} \right)\left( {...} \right)\) . Biểu thức điền vào dấu ba chấm là</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x + 12\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4x - 12$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x + 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4x + 12$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38979 loại 1.0--></span><div class="question c5bba38129104c05521d27ff2"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 30 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>sai.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${x^2} + 4x - {y^2} + 4 = \left( {x - y + 2} \right)\left( {x + y + 2} \right)$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {2{x^2} - y} \right)^2} - 64{y^2} = \left( {2{x^2} - 9y} \right)\left( {2{x^2} + 7y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - {x^3} + 6{x^2}y - 12x{y^2} + 8{y^3} = {\left( {2y - x} \right)^3}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\;{x^8} - {y^8} = {\left( {{x^4}} \right)^2} - {\left( {{y^4}} \right)^2} = \left( {{x^4} + {y^4}} \right)\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38980 loại 1.0--></span><div class="question c5bba38789104c05521d27ff5"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 31 : </strong> </span><p><span style="font-size: medium;">Có bao nhiêu giá trị của \(x\)  thỏa mãn \({\left( {x + 5} \right)^2} - 2\left( {x + 5} \right)\left( {x - 2} \right) + {\left( {x - 2} \right)^2} = 49\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$1$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$2$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Vô số</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38981 loại 1.0--></span><div class="question c5bba38d09104c05521d27ff8"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 32 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức \(B = (x - 2)\left( {{x^2} + 2x + 4} \right) - x\left( {x - 1} \right)\left( {x + 1} \right) + 3x\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x-8$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$8-4x$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$8-x$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4x - 8\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38986 loại 1.0--></span><div class="question c5bba3a469104c05521d28007"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 33 : </strong> </span><p><span style="font-size: medium;">Tìm giá trị của $x$ thỏa mãn \(x\left( {2x - 7} \right) - 4x + 14 = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;"><strong>\(x = \dfrac{7}{2}\) </strong>hoặc \(x =  - 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{{ - 7}}{2}\) hoặc \(x = 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{7}{2}\) hoặc \(x = 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;"><strong>\(x = \dfrac{{ - 7}}{2}\) </strong>hoặc \(x =  - 2\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38988 loại 1.0--></span><div class="question c5bba3ab39104c05521d2800d"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 34 : </strong> </span><p><span style="font-size: medium;">Chọn câu đúng nhất:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^2} - 2x - 4{y^2} - 4y = \left( {x - 2y - 2} \right)\left( {x + 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^2} + {y^2}x + {x^2}y + xy - x - y = \left( {x + xy - 1} \right)\left( {x + y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Cả A, B đều đúng</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Cả A, B đều sai</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38989 loại 1.0--></span><div class="question c5bba3b239104c05521d28010"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 35 : </strong> </span><p><span style="font-size: medium;">Tổng các giá trị của \(x\) thỏa mãn \(x\left( {x - 1} \right)\left( {x + 1} \right) + {x^2} - 1 = 0\)  là</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(0\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38994 loại 1.0--></span><div class="question c5bba3c789104c05521d2801f"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 36 : </strong> </span><p><span style="font-size: medium;">Tính giá trị của biểu thức \(B = {x^6} - 2{x^4} + {x^3} + {x^2} - x\) khi \({x^3} - x = 6\):</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$36$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$42$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$48$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$56$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38996 loại 1.0--></span><div class="question c5bba3d2f9104c05521d28025"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 37 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \(\;2{x^3}y - 2x{y^3} - 4x{y^2} - 2xy\) thành nhân tử  ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2xy\left( {x - y - 1} \right)\left( {x + y + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2xy\left( {x - y - 1} \right)\left( {x + y - 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xy\left( {x - y - 1} \right)\left( {x + y + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2xy\left( {x - y - 1} \right)\left( {x - y + 1} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 38998 loại 1.0--></span><div class="question c5bba3d879104c05521d2802b"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 38 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>sai:</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^4}\left( {x - y} \right) - x + y = \left( {2x - 1} \right)\left( {2x + 1} \right)\left( {4{x^2} + 1} \right)\left( {x - y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^3} - 54{y^3} = 2\left( {2x - 3y} \right)\left( {4{x^2} + 6xy + 9{y^2}} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^3} - 54{y^3} = 2\left( {2x - 3y} \right){\left( {2x + 3y} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^4}\left( {x - y} \right) - x + y = \left( {4{x^2} - 1} \right)\left( {4{x^2} + 1} \right)\left( {x - y} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39000 loại 1.0--></span><div class="question c5bba3e5e9104c05521d28031"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 39 : </strong> </span><p><span style="font-size: medium;">Tìm $x$ biết \({\left( {2x - 3} \right)^2} - 4{x^2} + 9 = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{1}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - \dfrac{3}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{3}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{2}{3}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39001 loại 1.0--></span><div class="question c5bba3ed19104c05521d28034"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 40 : </strong> </span><p><span style="font-size: medium;">Tìm $x$ biết \({x^3} - {x^2} - x + 1 = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\) hoặc \(x =  - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 1\) hoặc \(x = 0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\) hoặc \(x = 0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39003 loại 1.0--></span><div class="question c5bba3f289104c05521d2803a"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 41 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức sau thành nhân tử: \({x^3} - 5x + 4\) ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x + 1} \right)\left( {{x^2} + x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - 1} \right)\left( {{x^2} - x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - 1} \right)\left( {{x^2} + x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - 1} \right)\left( {{x^2} + x + 4} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39004 loại 1.0--></span><div class="question c5bba3fb49104c05521d2803d"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 42 : </strong> </span><p><span style="font-size: medium;">Thực hiện phép tính: \(\left( {4{x^4} - 4{x^3} + 3x - 3} \right):\left( {x - 1} \right)\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^2} + 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^3} - 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^2} - 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^3} + 3$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39005 loại 1.0--></span><div class="question c5bba3fff9104c05521d28040"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 43 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức: $A = \dfrac{{4{x^3} - 5{x^2} + 1}}{{{x} - 1}}$</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} - x - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} + x - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} + x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} - x + 1\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39007 loại 1.0--></span><div class="question c5bba40a69104c05521d28046"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 44 : </strong> </span><p><span style="font-size: medium;">Thực hiện phép tính \(A = \left( {6{x^3} - 5{x^2} + 4x - 1} \right):\left( {2{x^2} - x + 1} \right)\) ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3x - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39009 loại 1.0--></span><div class="question c5bba410d9104c05521d2804c"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 45 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức thành nhân tử  ta được \({x^3} + 7{x^2} + 12x + 4 = \left( {x + 2} \right)\left( {{x^2} + a.x + 2} \right)\) . Khi đó giá trị của \(a\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(5\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 6\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 5\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39010 loại 1.0--></span><div class="question c5bba415a9104c05521d2804f"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 46 : </strong> </span><p><span style="font-size: medium;">Có bao nhiêu giá trị của $x$ thỏa mãn \(\,2{x^3}\left( {2x - 3} \right) - {x^2}\left( {4{x^2} - 6x + 2} \right) = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39012 loại 1.0--></span><div class="question c5bba41bb9104c05521d28055"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 47 : </strong> </span><p><span style="font-size: medium;">Giá trị nhỏ nhất của biểu thức \(A = {x^2} - x + 1\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{2}{4}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{3}{4}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{3}{4}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39013 loại 1.0--></span><div class="question c5bba420d9104c05521d28058"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 48 : </strong> </span><p><span style="font-size: medium;">Giá trị lớn nhất của biểu thức \(B =  - 9{x^2} + 2x - \dfrac{2}{9}\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{2}{9}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{2}{9}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{1}{9}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{1}{9}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39014 loại 1.0--></span><div class="question c5bba42619104c05521d2805b"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 49 : </strong> </span><p><span style="font-size: medium;">Tính giá trị biểu thức \(P = \left( { - 4{x^3}{y^3} + {x^3}{y^4}} \right):2x{y^2} - xy\left( {2x - xy} \right)\) cho \(x = 1,y = \dfrac{{ - 1}}{2}\);</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P =  - \dfrac{{19}}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P = \dfrac{{19}}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P = \dfrac{8}{{19}}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P = \dfrac{9}{8}\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39016 loại 1.0--></span><div class="question c5bba42cb9104c05521d28061"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 50 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \({x^8} + {x^4} + 1\)  thành nhân tử ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} - x - 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} + x + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} + {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} + x + 1} \right)\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39017 loại 1.0--></span><div class="question c5bba43459104c05521d28064"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 51 : </strong> </span><p><span style="font-size: medium;">Cho \(S = 1 + x + {x^2} + {x^3} + {x^4} + {x^5}\), chọn câu đúng</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^6} - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^6}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^6} + 1\)<strong>  </strong></span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^7} - 1\)</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39019 loại 1.0--></span><div class="question c5bba44089104c05521d2806a"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 52 : </strong> </span><p><span style="font-size: medium;">Tìm giá trị nhỏ nhất của biểu thức \(A = {x^2} + 2{y^2} - 2xy + 2x - 10y\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=-17$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=-3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=17$</span></p> </div> </li> </ul> </div><span style="font-size: medium;"><!--Câu 39021 loại 1.0--></span><div class="question c5bba44a09104c05521d28071"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 53 : </strong> </span><p><span style="font-size: medium;">Cho: \({a^3} + {b^3} + {c^3} = 3abc\) thì</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c\) hoặc \(a + b + c = 0\).</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c = 0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c\) hoặc \(a + b + c = 1\)</span></p> </div> </li> </ul> </div> <div id="sub-question-2"> <p id="question-title-idx-2" style="border-top: 1px dotted lightgrey; margin: 10px 0px 15px; padding-top: 15px;"><strong style="color: #2888e1;"><span style="font-size: medium;"> Lời giải và đáp án </span></strong></p> <span style="font-size: medium;"><!--Câu 38953 loại 1.0--></span><div class="question c5bba31109104c05521d27fa4"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 1 : </strong> </span><p><span style="font-size: medium;">Tích của đơn thức $x$ và đa thức $(1 – x)$ là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1 - 2x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x - {x^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^2} - x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^2} + x\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Muốn nhân một đơn thức với một đa thức, ta nhân đơn thức với từng hạng tử của đa thức rồi cộng các tích với nhau.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(x\left( {1 - x} \right) = x.1 - x.x = x - {x^2}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38954 loại 1.0--></span><div class="question c5bba31719104c05521d27fa7"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 2 : </strong> </span><p><span style="font-size: medium;">Tích của đa thức \(4{x^5} + 7{x^2}\) và đơn thức \(\left( { - 3{x^3}} \right)\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(12{x^8} + 21{x^5}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(12{x^8} + 21{x^6}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 12{x^8} + 21{x^5}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 12{x^8} - 21{x^5}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Muốn nhân một đơn thức với một đa thức, ta nhân đơn thức với từng hạng tử của đa thức rồi cộng các tích với nhau.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\left( {4{x^5} + 7{x^2}} \right).\left( { - 3{x^3}} \right) \)\(= 4{x^5}.\left( { - 3{x^3}} \right) + 7{x^2}.\left( { - 3{x^3}} \right) =  - 12{x^8} - 21{x^5}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38956 loại 1.0--></span><div class="question c5bba320f9104c05521d27fad"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 3 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức \(A = \left( {{x^2} + 2 - 2x} \right)\left( {{x^2} + 2 + 2x} \right) - {x^4}\) ta được kết quả là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 4\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A =  - 4$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 19\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A =  - 19\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Muốn nhân một đa thức với một đa thức, ta nhân mỗi hạng tử của đa thức này với từng hạng tử của đa thức kia rồi cộng các tích với nhau.</span></p> <p><span style="font-size: medium;">Hoặc sử dụng hằng đẳng thức $(a+b)(a-b)=a^2-b^2$ và $(a+b)^2=a^2+2ab+b^2$</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">$A = \left( {{x^2} + 2 - 2x} \right)\left( {{x^2} + 2 + 2x} \right) - {x^4} $$= {x^2}.{x^2} + 2.{x^2} + 2x.{x^2} + 2.{x^2} + 2.2 + 2.2x - 2x.{x^2} - 2.2x - 2x.2x - {x^4} $$=x^4+2x^2+2x^3+2x^2+4+4x-2x^3-4x-4x^2-x^4$$= 4$</span></p> <p><span style="font-size: medium;">Vậy $A = 4$.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38957 loại 1.0--></span><div class="question c5bba32509104c05521d27fb0"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 4 : </strong> </span><p><span style="font-size: medium;">Rút gọn đa thức \(16{x^2} - 4x + \dfrac{1}{4}\) ta được kết quả nào sau đây?</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {4x - \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {x - \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {4x + \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {x + \dfrac{1}{2}} \right)^2}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức \({\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(16{x^2} - 4x + \dfrac{1}{4} = {\left( {4x} \right)^2} - 2.4x.\dfrac{1}{2} + {\left( {\dfrac{1}{2}} \right)^2} = {\left( {4x - \dfrac{1}{2}} \right)^2}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38958 loại 1.0--></span><div class="question c5bba32959104c05521d27fb3"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 5 : </strong> </span><p><span style="font-size: medium;">Trong các khai triển hằng đẳng thức sau, khai triển nào sai?</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {A + B} \right)^2} = {A^2} + 2AB + {B^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {A - B} \right)^3} = {A^3} - 3{A^2}B - 3A{B^2} + {B^3}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({A^3} - {B^3} = \left( {A - B} \right)\left( {{A^2} + AB + {B^2}} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\({\left( {A - B} \right)^3} \)\(= {\left( {A + \left( { - B} \right)} \right)^3} \)\(= {A^3} + 3.{A^2}.\left( { - B} \right) + 3.A.{\left( { - B} \right)^2} + {\left( { - B} \right)^3}\)\( = {A^3} - 3{A^2}B + 3A{B^2} - {B^3}\)</span></p> <p><span style="font-size: medium;">\( \Rightarrow {\left( {A - B} \right)^3} \)\(= {A^3} - 3{A^2}B - 3A{B^2} + {B^3}\) là sai.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38959 loại 1.0--></span><div class="question c5bba32dc9104c05521d27fb6"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 6 : </strong> </span><p><span style="font-size: medium;">Cho biết \(3{y^2} - 3y\left( {y - 2} \right) = 36\). Giá trị của $y$ là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">5</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">6</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">7</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">8</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Biến đổi vế trái bằng cách sử dụng quy tắc nhân đơn thức với đa thức rồi cộng trừ các hạng tử đồng dạng</span></p> <p><span style="font-size: medium;">Từ đó tìm \(y.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}3{y^2} - 3y\left( {y - 2} \right) = 36\\ \Leftrightarrow 3{y^2} - 3y.y - 3y\left( { - 2} \right) = 36\\ \Leftrightarrow 3{y^2} - 3{y^2} + 6y = 36\\ \Leftrightarrow 6y = 36 \\\Leftrightarrow y = 6\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38960 loại 1.0--></span><div class="question c5bba33239104c05521d27fb9"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 7 : </strong> </span><p><span style="font-size: medium;">Giá trị của biểu thức \(A = 2x\left( {3x - 1} \right) - 6x\left( {x + 1} \right) - \left( {3 - 8x} \right)\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 16x - 3\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 3\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 16x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Đáp án khác</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng quy tắc nhân đơn thức với đa thức rồi cộng trừ các hạng tử đồng dạng</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,A = 2x\left( {3x - 1} \right) - 6x\left( {x + 1} \right) - \left( {3 - 8x} \right)\\ \Leftrightarrow A = 2x.3x - 2x.1 - 6x.x - 6x.1 - 3 + 8x\\ \Leftrightarrow A = 6{x^2} - 2x - 6{x^2} - 6x - 3 + 8x\\ \Leftrightarrow A =  - 3\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38955 loại 1.0--></span><div class="question c5bba31c59104c05521d27faa"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 8 : </strong> </span><p><span style="font-size: medium;">Thực hiện phép tính \(\left( {{x^2} + x + 1} \right)\left( {{x^3} - {x^2} + 1} \right)\) ta được kết quả là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} + x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} - {x^4} + x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} + {x^4} + x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^5} - x - 1\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Muốn nhân một đa thức với một đa thức, ta nhân mỗi hạng tử của đa thức này với từng hạng tử của đa thức kia rồi cộng các tích với nhau.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">$\begin{array}{l}\;\;\;\left( {{x^2} + x + 1} \right)\left( {{x^3} - {x^2} + 1} \right)\\ = {x^2}.{x^3} - {x^2}.{x^2} + {x^2}.1 + x.{x^3} - x.{x^2} + x.1 + 1.{x^3} - 1.{x^2} + 1.1\\ = {x^5} - {x^4} + {x^2} + {x^4} - {x^3} + x + {x^3} - {x^2} + 1\\ = {x^5} + x + 1\end{array}$</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38961 loại 1.0--></span><div class="question c5bba337b9104c05521d27fbc"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 9 : </strong> </span><p><span style="font-size: medium;">Cho \(A = 5x\left( {4{x^2} - 2x + 1} \right) - 2x\left( {10{x^2} - 5x - 2} \right) - 9x + 1\). Chọn câu <strong>đúng.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 9x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 18x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(A = 9x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Giá trị của biểu thức $A$ không phụ thuộc vào biến $x.$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng quy tắc nhân đơn thức với đa thức rồi cộng trừ các hạng tử đồng dạng</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,A = 5x\left( {4{x^2} - 2x + 1} \right) - 2x\left( {10{x^2} - 5x - 2} \right) - 9x + 1\\ \Leftrightarrow A = 5x.4{x^2} - 5x.2x + 5x.1 - 2x.10{x^2} - 2x.\left( { - 5x} \right) - 2x\left( { - 2} \right) - 9x + 1\\ \Leftrightarrow A = 20{x^3}-{\rm{ }}10{x^2} + {\rm{ }}5x{\rm{ }}-{\rm{ }}20{x^3} + {\rm{ }}10{x^2} + {\rm{ }}4x - 9x + 1\\ \Leftrightarrow A = 9x - 9x + 1\\ \Leftrightarrow A = 1\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy giá trị của biểu thức $A$ không phụ thuộc vào biến $x.$</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38962 loại 1.0--></span><div class="question c5bba33b89104c05521d27fbf"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 10 : </strong> </span><p><span style="font-size: medium;">Tìm \(x\)  biết \(\left( {x + 2} \right)(x + 3) - \left( {x - 2} \right)\left( {x + 5} \right) = 6\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 5.\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 5.\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 10.\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 1.\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Biến đổi vế trái bằng cách sử dụng quy tắc nhân đa thức với đa thức rồi cộng trừ các hạng tử đồng dạng</span></p> <p><span style="font-size: medium;">Từ đó tìm \(x.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\left( {x + 2} \right)(x + 3) - \left( {x - 2} \right)\left( {x + 5} \right) = 6\\ \Leftrightarrow x.x + 3.x + 2.x + 2.3 - x.x - 5.x + 2.x + 2.5 = 6\\ \Leftrightarrow {x^2} + 3x + 2x + 6 - {x^2} - 5x + 2x + 10 = 6\\ \Leftrightarrow 2x + 16 = 6\\ \Leftrightarrow 2x =  - 10\\ \Leftrightarrow x =  - 5\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy \(x =  - 5.\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38963 loại 1.0--></span><div class="question c5bba33f39104c05521d27fc2"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 11 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức \({\left( {3x + 1} \right)^2} - 2\left( {3x + 1} \right)\left( {3x + 5} \right) + {\left( {3x + 5} \right)^2}\) ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(8\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(24\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức \({\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}{\left( {3x + 1} \right)^2} - 2\left( {3x + 1} \right)\left( {3x + 5} \right) + {\left( {3x + 5} \right)^2}\\ = {\left( {\left( {3x + 1} \right) - \left( {3x + 5} \right)} \right)^2}\\ = {\left( {3x + 1 - 3x - 5} \right)^2}\\ = {( - 4)^2} = 16\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38964 loại 1.0--></span><div class="question c5bba34369104c05521d27fc5"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 12 : </strong> </span><p><span style="font-size: medium;">Cho biết \({\left( {x + 4} \right)^2} - \left( {x - 1} \right)\left( {x + 1} \right) = 16\). Hỏi giá trị của \(x\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{1}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(8\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{1}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$ - 8\left( {x + 5} \right)$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng các hằng đẳng thức \({\left( {A + B} \right)^2} = {A^2} + 2AB + {B^2}\); \({A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)\)</span></p> <p><span style="font-size: medium;">Sau đó cộng trừ các hạng tử đồng dạng để tìm \(x.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}{\left( {x + 4} \right)^2} - \left( {x - 1} \right)\left( {x + 1} \right) = 16\\ \Leftrightarrow {x^2} + 2.x.4 + {4^2} - \left( {{x^2} - 1} \right) = 16\\ \Leftrightarrow {x^2} + 8x + 16 - {x^2} + 1 = 16\\ \Leftrightarrow 8x = 16 - 16 - 1\\ \Leftrightarrow 8x =  - 1\\ \Leftrightarrow x =  - \dfrac{1}{8}\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38965 loại 1.0--></span><div class="question c5bba34749104c05521d27fc8"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 13 : </strong> </span><p><span style="font-size: medium;">Cho $x + y = 3$. Tính giá trị của biểu thức: $A = {x^2} + 2xy + {y^2} - 4x - 4y + 1$.</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{1}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$ - 2$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức \({\left( {A + B} \right)^2} = {A^2} + 2AB + {B^2}\) và nhóm các hạng tử để biến đổi \(A\)  sao cho xuất hiện hạng tử \(x + y.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(A = {x^2} + 2xy + {y^2} - 4x - 4y + 1 \)\(= \left( {{x^2} + 2xy + {y^2}} \right) - \left( {4x + 4y} \right) + 1 \)\(= {\left( {x + y} \right)^2} - 4\left( {x + y} \right) + 1\)</span></p> <p><span style="font-size: medium;">Tại $x + y = 3$ , ta có: \(A = {3^2} - 4.3 + 1 =  - 2\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38966 loại 1.0--></span><div class="question c5bba34b89104c05521d27fcb"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 14 : </strong> </span><p><span style="font-size: medium;">Tìm \(x\) biết: \({\left( {x + 1} \right)^3} - {\left( {x - 1} \right)^3} - 6{\left( {x - 1} \right)^2} =  - 10\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - \dfrac{1}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 3$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng các hằng đẳng thức\({\left( {A + B} \right)^3} = {A^3} + 3{A^2}B + 3A{B^2} + {B^3}\); \({\left( {A - B} \right)^3} = {A^3} - 3{A^2}B + 3A{B^2} - {B^3}\);\({\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}\)</span></p> <p><span style="font-size: medium;">Sau đó cộng trừ các hạng tử đồng dạng để tìm \(x.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\({\left( {x + 1} \right)^3} - {\left( {x - 1} \right)^3} - 6{\left( {x - 1} \right)^2} =  - 10\)</span></p> <p><span style="font-size: medium;">\( {x^3} + 3{x^2} + 3x + 1 - \left( {{x^3} - 3{x^2} + 3x - 1} \right) - 6\left( {{x^2} - 2x + 1} \right) =  - 10\)</span></p> <p><span style="font-size: medium;">\({x^3} + 3{x^2} + 3x + 1 - {x^3} + 3{x^2} - 3x + 1 - 6{x^2} + 12x - 6 =  - 10\)<br />\(12x - 4 =  - 10\)</span></p> <p><span style="font-size: medium;">\(12x =  - 10 + 4\)</span></p> <p><span style="font-size: medium;">\(12x =  - 6\)</span></p> <p><span style="font-size: medium;">\( x = \dfrac{{ - 1}}{2}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38967 loại 1.0--></span><div class="question c5bba35009104c05521d27fce"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 15 : </strong> </span><p><span style="font-size: medium;">Kết quả phân tích đa thức \(6{x^2}y - 12x{y^2}\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x - 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x - y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x + 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6xy\left( {x + y} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng phương pháp đặt nhân tử chung</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(6{x^2}y - 12x{y^2} = 6xy.x - 6xy.2y = 6xy\left( {x - 2y} \right)\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38968 loại 1.0--></span><div class="question c5bba35429104c05521d27fd1"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 16 : </strong> </span><p><span style="font-size: medium;">Điền đơn thức vào chỗ trống: \(12{x^3}{y^2}{z^2} - 18{x^2}{y^2}{z^4} = ....\left( {2x - 3{z^2}} \right)\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6x{y^2}{z^2}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6{x^2}{y^2}{z^2}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6{y^2}{z^2}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$6{x^3}{y^2}{z^2}$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng phương pháp đặt nhân tử chung</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(12{x^3}{y^2}{z^2} - 18{x^2}{y^2}{z^4} = 6{x^2}{y^2}{z^2}.2x - 6{x^2}{y^2}{z^2}.3{z^2} = 6{x^2}{y^2}{z^2}\left( {2x - 3{z^2}} \right)\)</span></p> <p><span style="font-size: medium;">Vậy đơn thức điền vào chỗ trống là: \(6{x^2}{y^2}{z^2}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38969 loại 1.0--></span><div class="question c5bba35999104c05521d27fd4"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 17 : </strong> </span><p><span style="font-size: medium;">Tìm \(x\) biết: $2x\left( {x - 3} \right) + 5\left( {x - 3} \right) = 0$</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{5}{2}$ hoặc $x = 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x =  - \dfrac{5}{2}$ hoặc $x = 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{5}{2}$ hoặc $x =  - 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{2}{5}$ hoặc $x = 3$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng phương pháp đặt nhân tử chung đưa về phương trình tích \(A.B = 0 \Leftrightarrow \left[ \begin{array}{l}A = 0\\B = 0\end{array} \right.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\;\;\;2x\left( {x - 3} \right) + 5\left( {x - 3} \right) = 0\\ \Leftrightarrow \left( {2x + 5} \right)\left( {x - 3} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}2x + 5 = 0\\x - 3 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x =  - \dfrac{5}{2}\\x = 3\end{array} \right.\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy \(x =  - \dfrac{5}{2}\) hoặc $ x = 3$</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38970 loại 1.0--></span><div class="question c5bba35e09104c05521d27fd7"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 18 : </strong> </span><p><span style="font-size: medium;">Tính giá trị của biểu thức $A = x\left( {x - 2009} \right) - y\left( {2009 - x} \right)$ tại $x = 3009$ và $y = 1991$:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$5000000$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$500000$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$50000$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$5000$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng phương pháp đặt nhân tử chung để thu gọn \(A.\) Sau đó thay $x = 3009$ và $y = 1991$  để tính toán.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\;\;\;A = x\left( {x - 2009} \right) - y\left( {2009 - x} \right)\\ \Leftrightarrow A = x\left( {x - 2009} \right) + y\left( {x - 2009} \right)\\ \Leftrightarrow A = \left( {x + y} \right)\left( {x - 2009} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">Với $x = 3009$ và $y = 1991$, giá trị của biểu thức là:</span></p> <p><span style="font-size: medium;">\(A = \left( {3009 + 1991} \right)\left( {3009 - 2009} \right) = 5000.1000 = 5000000\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38971 loại 1.0--></span><div class="question c5bba362f9104c05521d27fda"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 19 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>sai.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(15{x^2} + 10xy = 5x\left( {3x + 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(35x\left( {y - 8} \right) - 14y\left( {8 - y} \right) = 7\left( {5x + 2y} \right)\left( {y - 8} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - x + 6{x^2}y - 12xy + 2 = \left( {6xy + 1} \right)\left( {x - 2} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^3} - {x^2} + x - 1 = \left( {{x^2} + 1} \right)\left( {x - 1} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng phương pháp đặt nhân tử chung và nhóm hạng tử thích hợp</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">Ta có</span></p> <p><span style="font-size: medium;">+) \(15{x^2} + 10xy = 5x.3x + 5x.2y = 5x\left( {3x + 2y} \right)\)</span></p> <p><span style="font-size: medium;">+) \(35x\left( {y - 8} \right) - 14y\left( {8 - y} \right) = 7.5x\left( {y - 8} \right) + 7.2y\left( {y - 8} \right) = \left( {7.5x + 7.2y} \right)\left( {y - 8} \right) = 7\left( {5x + 2y} \right)\left( {y - 8} \right)\)</span></p> <p><span style="font-size: medium;">+)</span></p> <p><span style="font-size: medium;">\(\begin{array}{l} - x + 6{x^2}y - 12xy + 2\\ = \left( {6{x^2}y - 12xy} \right) - \left( {x - 2} \right)\\ = \left( {6xy.x - 6xy.2} \right) - \left( {x - 2} \right)\\ = 6xy\left( {x - 2} \right) - \left( {x - 2} \right)\\ = \left( {6xy - 1} \right)\left( {x - 2} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">+)</span></p> <p><span style="font-size: medium;">\(\begin{array}{l}\;{x^3} - {x^2} + x - 1\\ = {x^2}.x - {x^2} + x - 1\\ = {x^2}\left( {x - 1} \right) + \left( {x - 1} \right)\\ = \left( {{x^2} + 1} \right)\left( {x - 1} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy A, B, D đúng, <strong>C </strong>sai.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38972 loại 1.0--></span><div class="question c5bba36749104c05521d27fdd"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 20 : </strong> </span><p><span style="font-size: medium;">Giá trị lớn nhất của \(x\)  thỏa mãn phương trình \(\;7{x^2}\left( {x - 7} \right) + 5x\left( {7 - x} \right) = 0\) là</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = \dfrac{5}{7}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 7$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 0$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x = 8$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">+ Sử dụng phương pháp đặt nhân tử chung để đưa phương trình về dạng \(A.B = 0 \Leftrightarrow \left[ \begin{array}{l}A = 0\\B = 0\end{array} \right.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}7{x^2}\left( {x - 7} \right) + 5x\left( {7 - x} \right) = 0\\ \Leftrightarrow 7x.x\left( {x - 7} \right) - 5.x\left( {x - 7} \right) = 0\\ \Leftrightarrow \left( {7x.x - 5.x} \right)\left( {x - 7} \right) = 0\\ \Leftrightarrow x\left( {7x - 5} \right)\left( {x - 7} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}x = 0\\7x - 5 = 0\\x - 7 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = 0\\x = \dfrac{5}{7}\\x = 7\end{array} \right.\end{array}\)</span></p> <p><span style="font-size: medium;">Giá trị lớn nhất của \(x\)  thỏa mãn đề bài là \(x = 7.\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38974 loại 1.0--></span><div class="question c5bba370b9104c05521d27fe3"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 21 : </strong> </span><p><span style="font-size: medium;">Đa thức \(12x - 9 - 4{x^2}\) được phân tích thành:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {2x - 3} \right)\left( {2x + 3} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - {\left( {2x - 3} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {3 - 2x} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - {\left( {2x + 3} \right)^2}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức \({\left( {A - B} \right)^2} = {A^2} - 2AB + {B^2}\) để phân tích đa thức thành nhân tử</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(12x - 9 - 4{x^2} =  - \left( {4{x^2} - 12x + 9} \right) =  - \left( {{{\left( {2x} \right)}^2} - 2.2x.3 + {3^2}} \right) =  - {\left( {2x - 3} \right)^2}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38976 loại 1.0--></span><div class="question c5bba37589104c05521d27fe9"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 22 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \({x^3} - 6{x^2}y + 12x{y^2} - 8{y^3}\) thành nhân tử:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {x - y} \right)^3}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${\left( {2x - y} \right)^3}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${x^3} - {\left( {2y} \right)^3}$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${\left( {x - 2y} \right)^3}$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức \({\left( {A - B} \right)^3} = {A^3} - 3{A^2}B + 3A{B^2} - {B^3}\) để phân tích đa thức thành nhân tử</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\({x^3} - 6{x^2}y + 12x{y^2} - 8{y^3} = {x^3} - 3.{x^2}.\left( {2y} \right) + 3.x.{\left( { 2y} \right)^2} - {\left( { 2y} \right)^3} = {\left( {x - 2y} \right)^3}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38983 loại 1.0--></span><div class="question c5bba393f9104c05521d27ffe"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 23 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức thành nhân tử: \(5{x^2} + 10xy - 4x - 8y\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {5x - 2y} \right)\left( {x + 4y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {5x + 4} \right)\left( {x - 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x + 2y} \right)\left( {5x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {5x - 4} \right)\left( {x - 2y} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Nhóm hạng tử thứ 1 với hạng tử thứ 2 và nhóm hạng tử thứ 3 với hạng tử thứ 4 để xuất hiện nhân tử chung.</span></p> <p><span style="font-size: medium;">Đặt nhân tử chung để được tích của các đa thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,5{x^2} + 10xy - 4x - 8y = \left( {5{x^2} + 10xy} \right) - \left( {4x + 8y} \right)\\ = 5x\left( {x + 2y} \right) - 4\left( {x + 2y} \right) = \left( {5x - 4} \right)\left( {x + 2y} \right)\end{array}\)</span></p> </div> </div> <div class="solution-suggesstion"> <div class="solution-suggesstion-title mark-title-essay"><span style="font-size: medium;"><i class="fa-solid fa-key" style="color: #ffd43b;"></i> Chú ý</span></div> <div> <p><span style="font-size: medium;">Học sinh cần chú ý khi nhóm các hạng tử và đằng trước biểu thức có dấu trừ ta cần đổi dấu các hạng tử khi đưa vào trong ngoặc.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38985 loại 1.0--></span><div class="question c5bba39c49104c05521d28004"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 24 : </strong> </span><p><span style="font-size: medium;">Điền vào chỗ trống: \(3{x^2} + 6x{y^2} - 3{y^2} + 6{x^2}y = 3\left( {...} \right)\left( {x + y} \right)\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><strong><span style="font-size: medium;">\(\left( {x + y + 2xy} \right)\)</span></strong></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - y + 2xy} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - y + xy} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - y + 3xy} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">- Sử dụng phương pháp giao hoán, kết hợp để sắp xếp các hạng tử.</span></p> <p><span style="font-size: medium;">- Nhóm hạng tử thứ 1 với hạng tử thứ 3 và nhóm hạng tử thứ 2 với hạng tử thứ 4 để xuất hiện nhân tử chung.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung để được tích của các đa thức.</span></p> <p><span style="font-size: medium;">- So sánh với đề bài để tìm ra đa thức cần điền vào chỗ trống.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,3{x^2} + 6x{y^2} - 3{y^2} + 6{x^2}y = \left( {3{x^2} - 3{y^2}} \right) + \left( {6x{y^2} + 6{x^2}y} \right)\\ = 3\left( {{x^2} - {y^2}} \right) + 6xy\left( {y + x} \right) = 3\left( {x - y} \right)\left( {x + y} \right) + 6xy\left( {x + y} \right)\\ = \left[ {3\left( {x - y} \right) + 6xy} \right]\left( {x + y} \right) = 3\left( {x - y + 2xy} \right)\left( {x + y} \right).\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy chỗ trống là \(\left( {x - y + 2xy} \right)\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38991 loại 1.0--></span><div class="question c5bba3b899104c05521d28016"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 25 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \(m.{n^3} - 1 + m - {n^3}\) thành nhân tử, ta được:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {m - 1} \right)\left( {n + 1} \right)\left( {{n^2} - n + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({n^2}\left( {n + 1} \right)\left( {m - 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {m + 1} \right)\left( {{n^2} + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{n^3} - 1} \right)\left( {m - 1} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp nhằm xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung để được tích các đa thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,m.{n^3} - 1 + m - {n^3}\\ = \left( {m{n^3} - {n^3}} \right) + \left( {m - 1} \right)\\ = {n^3}\left( {m - 1} \right) + \left( {m - 1} \right)\\ = \left( {{n^3} + 1} \right)\left( {m - 1} \right)\\ = \left( {n + 1} \right)\left( {{n^2} - n + 1} \right)\left( {m - 1} \right).\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38992 loại 1.0--></span><div class="question c5bba3bf49104c05521d28019"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 26 : </strong> </span><p><span style="font-size: medium;">Điền vào chỗ trống \(4{x^2} + 4x - {y^2} + 1 = \left( {...} \right)\left( {2x + y + 1} \right)\):</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x + y + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x - y + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x - y\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x + y\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp để xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung để được tích các đa thức.</span></p> <p><span style="font-size: medium;"><strong>- </strong>So sánh với yêu cầu của đề bài để chọn đáp án đúng.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,4{x^2} + 4x - {y^2} + 1\\ = \left( {{{\left( {2x} \right)}^2} + 2.2x + 1} \right) - {y^2}\\ = {\left( {2x + 1} \right)^2} - {y^2}\\ = \left( {2x + 1 - y} \right)\left( {2x + 1 + y} \right)\\ = \left( {2x - y + 1} \right)\left( {2x + y + 1} \right).\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy đa thức trong chỗ trống là \(2x - y + 1\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38999 loại 1.0--></span><div class="question c5bba3de89104c05521d2802e"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 27 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>đúng.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = {x^2}{\left( {x + 2} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = {x^2}{\left( {x - 2} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = {x^2}\left( {x - 2} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^4} - 4{x^3} + 4{x^2} = x{\left( {x - 2} \right)^2}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Đặt nhân tử chung, dùng hằng đẳng thức để phân tích</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}{x^4} - 4{x^3} + 4{x^2}\\ = {x^2}\left( {{x^2} - 4x + 4} \right)\\ = {x^2}\left( {{x^2} - 2.2.x + {2^2}} \right)\\ = {x^2}{\left( {x - 2} \right)^2}.\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38973 loại 1.0--></span><div class="question c5bba36c99104c05521d27fe0"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 28 : </strong> </span><p><span style="font-size: medium;">Có bao nhiêu giá trị của \(x\) thỏa mãn \({x^3} - 3{x^2} + 3 - x = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$1$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$2$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">+ Sử dụng phương pháp nhóm hạng tử và đặt nhân tử chung để đưa phương trình về dạng \(A.B = 0 \Leftrightarrow \left[ \begin{array}{l}A = 0\\B = 0\end{array} \right.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}{x^3} - 3{x^2} + 3 - x = 0\\ \Leftrightarrow {x^2}.x - 3.{x^2} + \left( {3 - x} \right) = 0\\ \Leftrightarrow {x^2}\left( {x - 3} \right) - \left( {x - 3} \right) = 0\\ \Leftrightarrow \left( {{x^2} - 1} \right)\left( {x - 3} \right) = 0\\ \Leftrightarrow \left( {x - 1} \right)\left( {x + 1} \right)\left( {x - 3} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}x - 1 = 0\\x + 1 = 0\\x - 3 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = 1\\x =  - 1\\x = 3\end{array} \right.\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy $x = 1$ hoặc $x = 3$ hoặc \(x =  - 1\).</span></p> <p><span style="font-size: medium;">Vậy có ba giá trị của \(x\) thỏa mãn đề bài.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38977 loại 1.0--></span><div class="question c5bba37aa9104c05521d27fec"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 29 : </strong> </span><p><span style="font-size: medium;">Cho  \(4{x^2} - 25 - \left( {2x + 7} \right)\left( {5 - 2x} \right) = \left( {2x - 5} \right)\left( {...} \right)\) . Biểu thức điền vào dấu ba chấm là</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2x + 12\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4x - 12$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x + 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4x + 12$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức \({A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)\) và phương pháp đặt nhân tử chung để phân tích đa thức thành nhân tử</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\;4{x^2} - 25 - \left( {2x + 7} \right)\left( {5 - 2x} \right)\\ = {\left( {2x} \right)^2} - {5^2} - \left( {2x + 7} \right)\left( {5 - 2x} \right)\\ = \left( {2x - 5} \right)\left( {2x + 5} \right) - \left( {2x + 7} \right)\left( {5 - 2x} \right)\\ = \left( {2x - 5} \right)\left( {2x + 5} \right) + \left( {2x + 7} \right)\left( {2x - 5} \right)\\ = \left( {2x - 5} \right)\left( {2x + 5 + 2x + 7} \right) = \left( {2x - 5} \right)\left( {4x + 12} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">Biểu thức cần điền là \(4x + 12.\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38979 loại 1.0--></span><div class="question c5bba38129104c05521d27ff2"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 30 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>sai.</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">${x^2} + 4x - {y^2} + 4 = \left( {x - y + 2} \right)\left( {x + y + 2} \right)$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({\left( {2{x^2} - y} \right)^2} - 64{y^2} = \left( {2{x^2} - 9y} \right)\left( {2{x^2} + 7y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - {x^3} + 6{x^2}y - 12x{y^2} + 8{y^3} = {\left( {2y - x} \right)^3}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\;{x^8} - {y^8} = {\left( {{x^4}} \right)^2} - {\left( {{y^4}} \right)^2} = \left( {{x^4} + {y^4}} \right)\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng các phương pháp đặt nhân tử chung, dùng hằng đẳng thức, thêm bớt hạng tử .. và phối hợp nhiều phương pháp để phân tích.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\( + )\;{x^2} + 4x - {y^2} + 4 = \left( {{x^2} + 4x + 4} \right) - {y^2} = \left( {{x^2} + 2.2.x + {2^2}} \right) - {y^2} = {\left( {x + 2} \right)^2} - {y^2} = \left( {x - y + 2} \right)\left( {x + y + 2} \right)\)</span></p> <p><span style="font-size: medium;">\( + )\;{\left( {2{x^2} - y} \right)^2} - 64{y^2} = {\left( {2{x^2} - y} \right)^2} - {\left( {8y} \right)^2} = \left( {2{x^2} - y - 8y} \right)\left( {2{x^2} - y + 8y} \right) = \left( {2{x^2} - 9y} \right)\left( {2{x^2} + 7y} \right)\)</span></p> <p><span style="font-size: medium;">\( + )\; - {x^3} + 6{x^2}y - 12x{y^2} + 8{y^3} = {\left( { - x} \right)^3} + 3.{x^2}.2y + 3.\left( { - x} \right).{\left( {2y} \right)^2} + {\left( {2y} \right)^3} = {\left( { - x + 2y} \right)^3} = {\left( {2y - x} \right)^3}\)</span></p> <p><span style="font-size: medium;">\( + )\;{x^8} - {y^8} = {\left( {{x^4}} \right)^2} - {\left( {{y^4}} \right)^2} = \left( {{x^4} + {y^4}} \right)\left( {{x^4} - {y^4}} \right)\)</span></p> <p><span style="font-size: medium;">\( = \left( {{x^4} + {y^4}} \right)\left( {{x^2} + {y^2}} \right)\left( {{x^2} - {y^2}} \right) = \left( {{x^4} + {y^4}} \right)\left( {{x^2} + {y^2}} \right)\left( {x + y} \right)\left( {x - y} \right)\)</span></p> <p><span style="font-size: medium;">Nên A, B, C đúng. <strong>D </strong>sai.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38980 loại 1.0--></span><div class="question c5bba38789104c05521d27ff5"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 31 : </strong> </span><p><span style="font-size: medium;">Có bao nhiêu giá trị của \(x\)  thỏa mãn \({\left( {x + 5} \right)^2} - 2\left( {x + 5} \right)\left( {x - 2} \right) + {\left( {x - 2} \right)^2} = 49\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$1$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$2$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Vô số</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng  đẳng thức  để biến đổi vế trái từ đó đưa về dạng \({A^2} = {m^2}\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">$\begin{array}{l}{\left( {x + 5} \right)^2} - 2\left( {x + 5} \right)\left( {x - 2} \right) + {\left( {x - 2} \right)^2} = 49\\ \Leftrightarrow {\left( {\left( {x + 5} \right) - \left( {x - 2} \right)} \right)^2} = 49\\ \Leftrightarrow {\left( {x + 5 - x + 2} \right)^2} = 49\\ \Leftrightarrow {7^2} = 49\end{array}$</span></p> <p><span style="font-size: medium;">Vậy với mọi \(x\) đều thỏa mãn.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38981 loại 1.0--></span><div class="question c5bba38d09104c05521d27ff8"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 32 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức \(B = (x - 2)\left( {{x^2} + 2x + 4} \right) - x\left( {x - 1} \right)\left( {x + 1} \right) + 3x\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$x-8$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$8-4x$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$8-x$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4x - 8\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng  đẳng thức  \({A^3} + {B^3} = \left( {A + B} \right)\left( {{A^2} - AB + {B^2}} \right)\) và  \({A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right)\) để biến đổi và rút gọn \(B.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}B = \left( {x - 2} \right)\left( {{x^2} + 2x + 4} \right) - x\left( {x - 1} \right)\left( {x + 1} \right) + 3x\\B = \left( {x - 2} \right)\left( {{x^2} + x.2 + {2^2}} \right) - x\left( {{x^2} - 1} \right) + 3x\\B = {x^3} - {2^3} - x.{x^2} + x.1 + 3x\\B = {x^3} - 8 - {x^3} + x + 3x\\B = 4x - 8\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38986 loại 1.0--></span><div class="question c5bba3a469104c05521d28007"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 33 : </strong> </span><p><span style="font-size: medium;">Tìm giá trị của $x$ thỏa mãn \(x\left( {2x - 7} \right) - 4x + 14 = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;"><strong>\(x = \dfrac{7}{2}\) </strong>hoặc \(x =  - 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{{ - 7}}{2}\) hoặc \(x = 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{7}{2}\) hoặc \(x = 2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;"><strong>\(x = \dfrac{{ - 7}}{2}\) </strong>hoặc \(x =  - 2\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Nhóm hạng tử để xuất hiện nhân tử chung.</span></p> <p><span style="font-size: medium;">Đặt nhân tử chung để được tích của các đa thức.</span></p> <p><span style="font-size: medium;">Để tích các đa thức bằng 0 thì giá trị từng đa thức phải bằng 0.</span></p> <p><span style="font-size: medium;">Suy ra giá trị x cần tìm.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,\,x\left( {2x - 7} \right) - 4x + 14 = 0\\ \Leftrightarrow x\left( {2x - 7} \right) - 2\left( {2x - 7} \right) = 0\\ \Leftrightarrow \left( {2x - 7} \right)\left( {x - 2} \right) = 0\\ \Leftrightarrow \left( {2x - 7} \right)\left( {x - 2} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}2x - 7 = 0\\x - 2 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = \dfrac{7}{2}\\x = 2\end{array} \right..\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy \(x = \dfrac{7}{2}\) hoặc \(x = 2\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38988 loại 1.0--></span><div class="question c5bba3ab39104c05521d2800d"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 34 : </strong> </span><p><span style="font-size: medium;">Chọn câu đúng nhất:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^2} - 2x - 4{y^2} - 4y = \left( {x - 2y - 2} \right)\left( {x + 2y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\({x^2} + {y^2}x + {x^2}y + xy - x - y = \left( {x + xy - 1} \right)\left( {x + y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Cả A, B đều đúng</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">Cả A, B đều sai</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng phương pháp phân phối phép nhân và phép trừ, giao hoán, kết hợp để sắp xếp và tạo ra các hạng tử cần thiết.</span></p> <p><span style="font-size: medium;">Sau đó, nhóm hạng tử để xuất hiện nhân tử chung.</span></p> <p><span style="font-size: medium;">Đặt nhân tử chung để được tích của các đa thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l} + ){x^2} - 2x - 4{y^2} - 4y\\ = \left( {{x^2} - 4{y^2}} \right) - \left( {2x + 4y} \right)\\ = \left( {x - 2y} \right)\left( {x + 2y} \right) - 2\left( {x + 2y} \right)\\ = \left( {x - 2y - 2} \right)\left( {x + 2y} \right).\end{array}\)<strong>                                       </strong></span></p> <p><span style="font-size: medium;">\(\begin{array}{l} + )\;{x^2} + {y^2}x + {x^2}y + xy - x - y\\ = \left( {{x^2} + xy} \right) + \left( {{y^2}x + {x^2}y} \right) - \left( {x + y} \right)\\ = x\left( {x + y} \right) + xy\left( {y + x} \right) - \left( {x + y} \right)\\ = \left( {x + xy - 1} \right)\left( {x + y} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy A, B đều đúng.</span></p> </div> </div> <div class="solution-suggesstion"> <div class="solution-suggesstion-title mark-title-essay"><span style="font-size: medium;"><i class="fa-solid fa-key" style="color: #ffd43b;"></i> Chú ý</span></div> <div> <p><span style="font-size: medium;">Học sinh thường hay mắc phải sai lầm là khi đặt nhân tử chung không chú ý đến dấu của hạng tử dẫn đến nhầm dấu. Ví dụ khi đặt \( - x - y =  - \left( {x - y} \right)\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38989 loại 1.0--></span><div class="question c5bba3b239104c05521d28010"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 35 : </strong> </span><p><span style="font-size: medium;">Tổng các giá trị của \(x\) thỏa mãn \(x\left( {x - 1} \right)\left( {x + 1} \right) + {x^2} - 1 = 0\)  là</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(0\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp nhằm xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> <p><span style="font-size: medium;">- Từ đó đưa về dạng \(A.B = 0 \Leftrightarrow \left[ \begin{array}{l}A = 0\\B = 0\end{array} \right.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}x(x - 1)\left( {x + 1} \right) + {x^2} - 1 = 0\\ \Leftrightarrow x\left( {x - 1} \right)\left( {x + 1} \right) + \left( {{x^2} - 1} \right) = 0\\ \Leftrightarrow x\left( {x - 1} \right)\left( {x + 1} \right) + \left( {x - 1} \right)\left( {x + 1} \right) = 0\\ \Leftrightarrow \left( {x + 1} \right)\left( {x - 1} \right)\left( {x + 1} \right) = 0\\ \Leftrightarrow {\left( {x + 1} \right)^2}\left( {x - 1} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}x + 1 = 0\\x - 1 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x =  - 1\\x = 1\end{array} \right.\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy \(x =  - 1\) hoặc \(x = 1\).</span></p> <p><span style="font-size: medium;">Tổng các giá trị của \(x\) là \(1 + \left( { - 1} \right) = 0.\)</span></p> </div> </div> <div class="solution-suggesstion"> <div class="solution-suggesstion-title mark-title-essay"><span style="font-size: medium;"><i class="fa-solid fa-key" style="color: #ffd43b;"></i> Chú ý</span></div> <div> <p><span style="font-size: medium;">HS dễ mắc phải một số sai lầm sau:</span></p> <p><span style="font-size: medium;">+) Chuyển vế không đổi dấu.</span></p> <p><span style="font-size: medium;">+) Khi nhóm các hạng tử đằng trước có dấu trừ cho vào trong ngoặc không đổi dấu.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38994 loại 1.0--></span><div class="question c5bba3c789104c05521d2801f"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 36 : </strong> </span><p><span style="font-size: medium;">Tính giá trị của biểu thức \(B = {x^6} - 2{x^4} + {x^3} + {x^2} - x\) khi \({x^3} - x = 6\):</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$36$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$42$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$48$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$56$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">+ Sử dụng phương pháp giao hoán, kết hợp và tách hạng tử (tách hạng tử thứ 2 thành 2 hạng tử giống nhau) để sắp xếp và tạo ra các hạng tử cần thiết.</span></p> <p><span style="font-size: medium;">+ Sau khi tách hạng tử, nhóm các hạng tử thích hợp để xuất hiện nhân tử chung giống với \({x^3} - x\).</span></p> <p><span style="font-size: medium;">+ Đặt nhân tử chung để được tích của các đa thức.</span></p> <p><span style="font-size: medium;">+ Sau đó thế biểu thức \({x^3} - x = 6\) vào biểu thức vừa biến đổi để tính giá trị biểu thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,\,B = {x^6} - 2{x^4} + {x^3} + {x^2} - x\\ \Leftrightarrow B = {x^6} - {x^4} - {x^4} + {x^3} + {x^2} - x\\ \Leftrightarrow B = \left( {{x^6} - {x^4}} \right) - \left( {{x^4} - {x^2}} \right) + \left( {{x^3} - x} \right)\\ \Leftrightarrow B = {x^3}\left( {{x^3} - x} \right) - x\left( {{x^3} - x} \right) + \left( {{x^3} - x} \right)\\ \Leftrightarrow B = \left( {{x^3} - x + 1} \right)\left( {{x^3} - x} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">Tại \({x^3} - x = 6\), ta có: \(B = \left( {6 + 1} \right).6 = 7.6 = 42\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38996 loại 1.0--></span><div class="question c5bba3d2f9104c05521d28025"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 37 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \(\;2{x^3}y - 2x{y^3} - 4x{y^2} - 2xy\) thành nhân tử  ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2xy\left( {x - y - 1} \right)\left( {x + y + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2xy\left( {x - y - 1} \right)\left( {x + y - 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xy\left( {x - y - 1} \right)\left( {x + y + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2xy\left( {x - y - 1} \right)\left( {x - y + 1} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp nhằm xuất hiện hằng đẳng thức hoặc nhân tử chung mới. Từ đó biến đổi tiếp để được tích các đa thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}2{x^3}y - 2x{y^3} - 4x{y^2} - 2xy\\ = 2xy\left( {{x^2} - {y^2} - 2y - 1} \right)\\ = 2xy\left[ {{x^2} - \left( {{y^2} + 2y + 1} \right)} \right]\\ = 2xy\left[ {{x^2} - {{\left( {y + 1} \right)}^2}} \right]\\ = 2xy\left( {x - y - 1} \right)\left( {x + y + 1} \right).\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 38998 loại 1.0--></span><div class="question c5bba3d879104c05521d2802b"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 38 : </strong> </span><p><span style="font-size: medium;">Chọn câu <strong>sai:</strong></span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^4}\left( {x - y} \right) - x + y = \left( {2x - 1} \right)\left( {2x + 1} \right)\left( {4{x^2} + 1} \right)\left( {x - y} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^3} - 54{y^3} = 2\left( {2x - 3y} \right)\left( {4{x^2} + 6xy + 9{y^2}} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^3} - 54{y^3} = 2\left( {2x - 3y} \right){\left( {2x + 3y} \right)^2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(16{x^4}\left( {x - y} \right) - x + y = \left( {4{x^2} - 1} \right)\left( {4{x^2} + 1} \right)\left( {x - y} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Dùng các hằng đẳng thức đáng nhớ, đặt nhân tử chung và nhóm hạng tử để phân tích</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l} + )\,16{x^4}\left( {x - y} \right) - x + y\\ = 16{x^4}\left( {x - y} \right) - \left( {x - y} \right)\\ = \left( {16{x^4} - 1} \right)\left( {x - y} \right)\\ = \left[ {{{\left( {2x} \right)}^4} - 1} \right]\left( {x - y} \right)\\ = \left[ {{{\left( {2x} \right)}^2} - 1} \right]\left[ {\left( {2{x^2}} \right) + 1} \right]\left( {x - y} \right)\\ = \left( {2x - 1} \right)\left( {2x + 1} \right)\left( {4{x^2} + 1} \right)\left( {x - y} \right).\end{array}\)</span></p> <p><span style="font-size: medium;">\(\begin{array}{l} + )\;16{x^3} - 54{y^3}\\ = 2\left( {8{x^3} - 27{y^3}} \right)\\ = 2\left[ {{{\left( {2x} \right)}^3} - {{\left( {3y} \right)}^3}} \right]\\ = 2\left( {2x - 3y} \right)\left[ {{{\left( {2x} \right)}^2} + 2x.3y + {{\left( {3y} \right)}^2}} \right]\\ = 2\left( {2x - 3y} \right)\left( {4{x^2} + 6xy + 9{y^2}} \right).\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy A, B, D đúng. C sai</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39000 loại 1.0--></span><div class="question c5bba3e5e9104c05521d28031"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 39 : </strong> </span><p><span style="font-size: medium;">Tìm $x$ biết \({\left( {2x - 3} \right)^2} - 4{x^2} + 9 = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{1}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - \dfrac{3}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{3}{2}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = \dfrac{2}{3}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp để xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung để được dạng $A.B.C = 0$</span></p> <p><span style="font-size: medium;">- Suy ra $A = 0 $ hoặc $B = 0$ hoặc $C = 0.$</span></p> <p><span style="font-size: medium;">- Suy ra các giá trị của $x$ cần tìm.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}{\left( {2x - 3} \right)^2} - 4{x^2} + 9 = 0\\ \Leftrightarrow {\left( {2x - 3} \right)^2} - \left( {4{x^2} - 9} \right) = 0\\ \Leftrightarrow {\left( {2x - 3} \right)^2} - \left( {{{\left( {2x} \right)}^2} - {3^2}} \right) = 0\\ \Leftrightarrow {\left( {2x - 3} \right)^2} - \left( {2x - 3} \right)\left( {2x + 3} \right) = 0\\ \Leftrightarrow \left( {2x - 3} \right)\left( {2x - 3 - 2x - 3} \right) = 0\\ \Leftrightarrow \left( {2x - 3} \right)\left( { - 6} \right) = 0\\ \Leftrightarrow 2x - 3 = 0\\ \Leftrightarrow x = \dfrac{3}{2}\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy \(x = \dfrac{3}{2}\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39001 loại 1.0--></span><div class="question c5bba3ed19104c05521d28034"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 40 : </strong> </span><p><span style="font-size: medium;">Tìm $x$ biết \({x^3} - {x^2} - x + 1 = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\) hoặc \(x =  - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x =  - 1\) hoặc \(x = 0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\) hoặc \(x = 0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(x = 1\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp để xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung để được dạng $A.B.C = 0$</span></p> <p><span style="font-size: medium;">- Suy ra $A = 0$ hoặc $B = 0$ hoặc $C = 0.$</span></p> <p><span style="font-size: medium;">- Suy ra các giá trị của $x$ cần tìm.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,{x^3} - {x^2} - x + 1 = 0\\ \Leftrightarrow \left( {{x^3} - {x^2}} \right) - \left( {x - 1} \right) = 0\\ \Leftrightarrow {x^2}\left( {x - 1} \right) - \left( {x - 1} \right) = 0\\ \Leftrightarrow \left( {{x^2} - 1} \right)\left( {x - 1} \right) = 0\end{array}\)</span></p> <p><span style="font-size: medium;">\(\begin{array}{l} \Leftrightarrow \left( {x - 1} \right)\left( {x + 1} \right)\left( {x - 1} \right) = 0\\ \Leftrightarrow {\left( {x - 1} \right)^2}\left( {x + 1} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l}x - 1 = 0\\x + 1 = 0\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}x = 1\\x =  - 1\end{array} \right.\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy \(x = 1\) hoặc \(x =  - 1\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39003 loại 1.0--></span><div class="question c5bba3f289104c05521d2803a"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 41 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức sau thành nhân tử: \({x^3} - 5x + 4\) ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x + 1} \right)\left( {{x^2} + x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - 1} \right)\left( {{x^2} - x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - 1} \right)\left( {{x^2} + x - 4} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {x - 1} \right)\left( {{x^2} + x + 4} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Tách 1 hạng tử thành nhiều hạng tử hoặc thêm, bớt cùng một hạng tử làm xuất hiện nhân tử chung hoặc các hằng đẳng thức.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp nhằm xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,{x^3} - 5x + 4\\ = {x^3} - x - 4x + 4\\ = x\left( {{x^2} - 1} \right) - 4\left( {x - 1} \right)\\ = x\left( {x - 1} \right)\left( {x + 1} \right) - 4\left( {x - 1} \right)\\ = \left( {x - 1} \right)\left[ {x\left( {x + 1} \right) - 4} \right]\\ = \left( {x - 1} \right)\left( {{x^2} + x - 4} \right).\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39004 loại 1.0--></span><div class="question c5bba3fb49104c05521d2803d"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 42 : </strong> </span><p><span style="font-size: medium;">Thực hiện phép tính: \(\left( {4{x^4} - 4{x^3} + 3x - 3} \right):\left( {x - 1} \right)\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^2} + 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^3} - 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^2} - 3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$4{x^3} + 3$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Đặt phép chia, thực hiện phép tính (Hoặc biến đổi số bị chia thành tích các đa thức trong đó có 1 đa thức giống số chia, sau đó thực hiện phép tính).</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <span style="font-size: medium;"><img src="https://cdn.vungoi.vn/vungoi/1538932620355_00.png" style="max-width: 100%;" /> </span><p><span style="font-size: medium;">$\left( {4{x^4} - 4{x^3} + 3x - 3} \right):\left( {x - 1} \right) = 4{x^3} + 3$</span></p> </div> </div> <div class="solution-suggesstion"> <div class="solution-suggesstion-title mark-title-essay"><span style="font-size: medium;"><i class="fa-solid fa-key" style="color: #ffd43b;"></i> Chú ý</span></div> <div> <p><span style="font-size: medium;">Các em có thể sử dụng cách làm sau</span></p> <p><span style="font-size: medium;">$\begin{array}{l}\,\,\,\,\left( {4{x^4} - 4{x^3} + 3x - 3} \right):\left( {x - 1} \right)\\ = \left( {4{x^3}\left( {x - 1} \right) + 3\left( {x - 1} \right)} \right):\left( {x - 1} \right)\\ = \left( {4{x^3} + 3} \right).\left( {x - 1} \right):\left( {x - 1} \right) = 4{x^3} + 3.\end{array}$</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39005 loại 1.0--></span><div class="question c5bba3fff9104c05521d28040"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 43 : </strong> </span><p><span style="font-size: medium;">Rút gọn biểu thức: $A = \dfrac{{4{x^3} - 5{x^2} + 1}}{{{x} - 1}}$</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} - x - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} + x - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} + x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(4{x^2} - x + 1\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Kết hợp các phương pháp phân tích đa thức thành nhân tử và thực hiện phép tính chia để thu được biểu thức rút gọn.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">$\begin{array}{l}A = \dfrac{{4{x^3} - 5{x^2} + 1}}{{x - 1}}\\\,\,\,\,\,\, = \dfrac{{4{x^3} - 4{x^2} - {x^2} + 1}}{{x - 1}}\\\,\,\,\,\,\, = \dfrac{{4{x^2}\left( {x - 1} \right) - \left( {{x^2} - 1} \right)}}{{x - 1}}\\\,\,\,\,\,\, = \dfrac{{4{x^2}\left( {x - 1} \right) - \left( {x - 1} \right)\left( {x + 1} \right)}}{{x - 1}}\\\,\,\,\,\,\, = \dfrac{{\left( {x - 1} \right)\left( {4{x^2} - x - 1} \right)}}{{x - 1}} = 4{x^2} - x - 1.\end{array}$</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39007 loại 1.0--></span><div class="question c5bba40a69104c05521d28046"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 44 : </strong> </span><p><span style="font-size: medium;">Thực hiện phép tính \(A = \left( {6{x^3} - 5{x^2} + 4x - 1} \right):\left( {2{x^2} - x + 1} \right)\) ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3x - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3x + 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3x\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Đặt tính theo hàng dọc rồi thực hiện phép chia để tìm thương</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\left( {6{x^3} - 5{x^2} + 4x - 1} \right):\left( {2{x^2} - x + 1} \right)\)</span></p><span style="font-size: medium;"><img src="https://cdn.vungoi.vn/vungoi/1538932877755_00.png" style="max-width: 100%;" /> </span><p><span style="font-size: medium;">\(\left( {6{x^3} - 5{x^2} + 4x - 1} \right):\left( {2{x^2} - x + 1} \right) = 3x - 1.\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39009 loại 1.0--></span><div class="question c5bba410d9104c05521d2804c"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 45 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức thành nhân tử  ta được \({x^3} + 7{x^2} + 12x + 4 = \left( {x + 2} \right)\left( {{x^2} + a.x + 2} \right)\) . Khi đó giá trị của \(a\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(5\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 6\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - 5\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(6\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Tách 1 hạng tử thành nhiều hạng tử hoặc thêm, bớt cùng một hạng tử làm xuất hiện nhân tử chung hoặc các hằng đẳng thức.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp nhằm xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l} + )\;{x^3} + 7{x^2} + 12x + 4\\ = {x^3} + 6{x^2} + {x^2} + 12x + 8 - 4\\ = \left( {{x^3} + 6{x^2} + 12x + 8} \right) + \left( {{x^2} - 4} \right)\\ = \left( {{x^3} + 3.2.{x^2} + {{3.2}^2}.x + {2^3}} \right) + \left( {{x^2} - 4} \right)\\ = {\left( {x + 2} \right)^3} + \left( {x - 2} \right)\left( {x + 2} \right)\\ = \left( {x + 2} \right)\left( {{{\left( {x + 2} \right)}^2} + x - 2} \right)\\ = \left( {x + 2} \right)\left( {{x^2} + 4x + 4 + x - 2} \right)\\ = \left( {x + 2} \right)\left( {{x^2} + 5x + 2} \right)\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39010 loại 1.0--></span><div class="question c5bba415a9104c05521d2804f"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 46 : </strong> </span><p><span style="font-size: medium;">Có bao nhiêu giá trị của $x$ thỏa mãn \(\,2{x^3}\left( {2x - 3} \right) - {x^2}\left( {4{x^2} - 6x + 2} \right) = 0\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(2\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(3\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">-Nhân đơn thức với đa thức rồi cộng trừ các hạng tử đồng dạng để biến đổi biểu thức thành tích các đa thức và đơn thức có dạng: $A.B = 0,$ suy ra $A = 0$ hoặc $B = 0,$ từ đó rút ra giá trị của $x$ cần tìm.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}2{x^3}\left( {2x - 3} \right) - {x^2}\left( {4{x^2} - 6x + 2} \right) = 0\\ \Leftrightarrow 4{x^4} - 6{x^3} - 4{x^4} + 6{x^3} - 2{x^2} = 0\\ \Leftrightarrow  - 2{x^2} = 0\\ \Leftrightarrow x = 0\end{array}\)</span></p> <p><span style="font-size: medium;">Vậy $x = 0.$</span></p> <p><span style="font-size: medium;">Có \(1\)  giá trị của \(x\)  thỏa mãn đề bài.</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39012 loại 1.0--></span><div class="question c5bba41bb9104c05521d28055"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 47 : </strong> </span><p><span style="font-size: medium;">Giá trị nhỏ nhất của biểu thức \(A = {x^2} - x + 1\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{2}{4}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{3}{4}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{3}{4}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Biến đổi đưa về dạng \({\left( {x - a} \right)^2} + m\)  rồi đánh giá \({\left( {x - a} \right)^2} + m \ge m\)</span></p> <p><span style="font-size: medium;">Giá trị nhỏ nhất của \({\left( {x - a} \right)^2} + m\)  là \(m \Leftrightarrow x = a.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}A = {x^2} - x + 1 = {x^2} - 2.x.\dfrac{1}{2} + {\left( {\dfrac{1}{2}} \right)^2} + \dfrac{3}{4} = {\left( {x - \dfrac{1}{2}} \right)^2} + \dfrac{3}{4} \ge \dfrac{3}{4}\\ \Rightarrow \;Min\;A = \dfrac{3}{4}\;\end{array}\)</span></p> <p><span style="font-size: medium;">Dấu “=” xảy ra khi \({\left( {x - \dfrac{1}{2}} \right)^2} = 0\) hay \(x = \dfrac{1}{2}\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39013 loại 1.0--></span><div class="question c5bba420d9104c05521d28058"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 48 : </strong> </span><p><span style="font-size: medium;">Giá trị lớn nhất của biểu thức \(B =  - 9{x^2} + 2x - \dfrac{2}{9}\) là:</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{2}{9}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{2}{9}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\dfrac{1}{9}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\( - \dfrac{1}{9}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : D</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Biến đổi đưa về dạng \( - {\left( {x - a} \right)^2} + m\)  rồi đánh giá \( - {\left( {x - a} \right)^2} + m \le m\)</span></p> <p><span style="font-size: medium;">Giá trị lớ nhất của \( - {\left( {x - a} \right)^2} + m\)  là \(m \Leftrightarrow x = a.\)</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(B =  - 9{x^2} + 2x - \dfrac{2}{9} \)\(=  - {\left( {3x} \right)^2} + 2.3x.\dfrac{1}{3} - {\left( {\dfrac{1}{3}} \right)^2} - \dfrac{1}{9} \)\(=  - \left( {{{\left( {3x} \right)}^2} - 2.3x.\dfrac{1}{3} + {{\left( {\dfrac{1}{3}} \right)}^2}} \right) - \dfrac{1}{9} \)\(=  - {\left( {3x - \dfrac{1}{3}} \right)^2} - \dfrac{1}{9} \le  - \dfrac{1}{9}\)</span></p> <p><span style="font-size: medium;">\( \Rightarrow \;Max\;B =  - \dfrac{1}{9}\)<strong>.</strong></span></p> <p><span style="font-size: medium;">Dấu “=” xảy ra khi \({\left( {3x - \dfrac{1}{3}} \right)^2} = 0\) hay \(x = \dfrac{1}{9}\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39014 loại 1.0--></span><div class="question c5bba42619104c05521d2805b"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 49 : </strong> </span><p><span style="font-size: medium;">Tính giá trị biểu thức \(P = \left( { - 4{x^3}{y^3} + {x^3}{y^4}} \right):2x{y^2} - xy\left( {2x - xy} \right)\) cho \(x = 1,y = \dfrac{{ - 1}}{2}\);</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P =  - \dfrac{{19}}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P = \dfrac{{19}}{8}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P = \dfrac{8}{{19}}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(P = \dfrac{9}{8}\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Rút gọn biểu thức đã cho, sau đó thay giá trị của biến vào biểu thức rút gọn để tìm ra giá trị của biểu thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,\,P = \left( { - 4{x^3}{y^3} + {x^3}{y^4}} \right):2x{y^2} - xy\left( {2x - xy} \right)\\ \Leftrightarrow P = \left( { - 4{x^3}{y^3}} \right):2x{y^2} + {x^3}{y^4}:2x{y^2} - xy.2x + xy.xy\\ \Leftrightarrow P =  - 2{x^2}y + \dfrac{1}{2}{x^2}{y^2} - 2{x^2}y + {x^2}{y^2}\\ \Leftrightarrow P = \dfrac{3}{2}{x^2}{y^2} - 4{x^2}y\\ \Leftrightarrow P = {x^2}y\left( {\dfrac{3}{2}y - 4} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">Tại \(x = 1,y = \dfrac{{ - 1}}{2}\), ta có: \(P = {1^2}.\left( {\dfrac{{ - 1}}{2}} \right)\left( {\dfrac{3}{2}\left( {\dfrac{{ - 1}}{2}} \right) - 4} \right) = \left( {\dfrac{{ - 1}}{2}} \right)\left( {\dfrac{{ - 3}}{4} - 4} \right) = \left( {\dfrac{{ - 1}}{2}} \right)\left( {\dfrac{{ - 19}}{4}} \right) = \dfrac{{19}}{8}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39016 loại 1.0--></span><div class="question c5bba42cb9104c05521d28061"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 50 : </strong> </span><p><span style="font-size: medium;">Phân tích đa thức \({x^8} + {x^4} + 1\)  thành nhân tử ta được</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} - x - 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} + x + 1} \right)\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(\left( {{x^4} + {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} + x + 1} \right)\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : C</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;"><strong>- </strong>Tách 1 hạng tử thành nhiều hạng tử hoặc thêm, bớt cùng một hạng tử làm xuất hiện nhân tử chung hoặc các hằng đẳng thức.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung, dùng các hằng đẳng thức đáng nhớ hoặc nhóm các hạng tử một cách thích hợp nhằm xuất hiện hằng đẳng thức hoặc nhân tử chung mới.</span></p> <p><span style="font-size: medium;">- Đặt nhân tử chung để được tích các đa thức.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}{x^8} + {x^4} + 1\\ = {x^8} + 2{x^4} + 1 - {x^4}\\ = \left( {{x^8} + 2{x^4} + 1} \right) - {x^4}\\ = \left[ {{{\left( {{x^4}} \right)}^2} + 2.{x^4}.1 + {1^2}} \right] - {x^4}\\ = {\left( {{x^4} + 1} \right)^2} - {\left( {{x^2}} \right)^2}\\ = \left( {{x^4} + 1 - {x^2}} \right)\left( {{x^4} + 1 + {x^2}} \right)\\ = \left( {{x^4} - {x^2} + 1} \right)\left( {{x^4} + 2{x^2} - {x^2} + 1} \right)\end{array}\)</span></p> <p><span style="font-size: medium;">\(\begin{array}{l} = \left( {{x^4} - {x^2} + 1} \right)\left[ {\left( {{{\left( {{x^2}} \right)}^2} + 2.1.{x^2} + 1} \right) - {x^2}} \right]\\ = \left( {{x^4} - {x^2} + 1} \right)\left[ {{{\left( {{x^2} + 1} \right)}^2} - {x^2}} \right]\\ = \left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} + 1 - x} \right)\left( {{x^2} + 1 + x} \right)\\ = \left( {{x^4} - {x^2} + 1} \right)\left( {{x^2} - x + 1} \right)\left( {{x^2} + x + 1} \right).\end{array}\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39017 loại 1.0--></span><div class="question c5bba43459104c05521d28064"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 51 : </strong> </span><p><span style="font-size: medium;">Cho \(S = 1 + x + {x^2} + {x^3} + {x^4} + {x^5}\), chọn câu đúng</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^6} - 1\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^6}\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^6} + 1\)<strong>  </strong></span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(xS - S = {x^7} - 1\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Thực hiện phép nhân đơn thức với đa thức để tìm ra đáp án đúng.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(xS = x.(1 + x + {x^2} + {x^3} + {x^4} + {x^5}) = x + {x^2} + {x^3} + {x^4} + {x^5} + {x^6}.\)</span></p> <p><span style="font-size: medium;">\( \Rightarrow xS - S = x + {x^2} + {x^3} + {x^4} + {x^5} + {x^6} - 1 - x - {x^2} - {x^3} - {x^4} - {x^5} = {x^6} - 1.\)</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39019 loại 1.0--></span><div class="question c5bba44089104c05521d2806a"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 52 : </strong> </span><p><span style="font-size: medium;">Tìm giá trị nhỏ nhất của biểu thức \(A = {x^2} + 2{y^2} - 2xy + 2x - 10y\)</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=-17$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=-3$</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">$A=17$</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : B</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">- Tách 1 hạng tử thành nhiều hạng tử hoặc thêm, bớt cùng một hạng tử một cách thích hợp để tách biểu thức đã cho thành dạng $C = a^2 + b^2 + c.$</span></p> <p><span style="font-size: medium;">- Khi đó, \(A \ge c\) với mọi $x.$</span></p> <p><span style="font-size: medium;">- Suy ra, giá trị nhỏ nhất của $A.$</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">\(\begin{array}{l}\,\,\,\,\,\,\,\,A = {x^2} + 2{y^2} - 2xy + 2x - 10y\\ \Leftrightarrow A = {x^2} + {y^2} + 1 - 2xy + 2x - 2y + {y^2} - 8y + 16 - 17\\ \Leftrightarrow A = \left( {{x^2} + {y^2} + {1^2} - 2.x.y + 2.x.1 - 2.y.1} \right) + \left( {{y^2} - 2.4.y + {4^2}} \right) - 17\\ \Leftrightarrow A = {\left( {x - y + 1} \right)^2} + {\left( {y - 4} \right)^2} - 17.\end{array}\)</span></p> <p><span style="font-size: medium;">Vì \(\left\{ \begin{array}{l}{\left( {x - y + 1} \right)^2} \ge 0\\{\left( {y - 4} \right)^2} \ge 0\end{array} \right.\) với mọi $x;y$ nên \(A \ge  - 17\) với mọi $x;y.$</span></p> <p><span style="font-size: medium;">\( \Rightarrow A =  - 17 \Leftrightarrow \left\{ \begin{array}{l}x - y + 1 = 0\\y - 4 = 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x = y - 1\\y = 4\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x = 3\\y = 4\end{array} \right.\)</span></p> <p><span style="font-size: medium;">Vậy $A$ đạt giá trị nhỏ nhất là \(A =  - 17\) tại \(\left\{ \begin{array}{l}x = 3\\y = 4\end{array} \right.\).</span></p> </div> </div> </div> </div><span style="font-size: medium;"><!--Câu 39021 loại 1.0--></span><div class="question c5bba44a09104c05521d28071"> <div class="question-content"> <div class="question-content-inner"> <span style="font-size: medium;"><strong class="question-index-number">Câu 53 : </strong> </span><p><span style="font-size: medium;">Cho: \({a^3} + {b^3} + {c^3} = 3abc\) thì</span></p> </div> </div> <ul class="dapan rows-4"> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">A.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c\) hoặc \(a + b + c = 0\).</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">B.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">C.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c = 0\)</span></p> </div> </li> <li style="align-items: flex-start; display: flex;"> <span class="span-answer" style="padding-top: 0px;"><span style="font-size: medium;">D.</span></span> <div style="width: 90%;"> <p><span style="font-size: medium;">\(a = b = c\) hoặc \(a + b + c = 1\)</span></p> </div> </li> </ul> <div class="loigiai"> <p><b style="color: black;"><span style="font-size: medium;">Đáp án : A</span></b></p> <div class="solution-suggesstion"> <div class="solution-suggesstion-title"><span style="font-size: medium;">Phương pháp giải : </span></div> <div> <p><span style="font-size: medium;">Sử dụng hằng đẳng thức: \({a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)\) để biến đổi giả thiết.</span></p> </div> </div> <div class="solution-detail"> <div class="solution-detail-title"><span style="font-size: medium;">Lời giải chi tiết : </span></div> <div> <p><span style="font-size: medium;">Từ đẳng thức đã cho suy ra \({a^3} + {b^3} + {c^3} - 3abc = 0\)</span></p> <p><span style="font-size: medium;">${b^3} + {c^3} = \left( {b + c} \right)\left( {{b^2} + {c^2} - bc} \right) $$= \left( {b + c} \right)\left[ {{{\left( {b + c} \right)}^2} - 3bc} \right] $$= {\left( {b + c} \right)^3} - 3bc\left( {b + c} \right)$</span></p> <p><span style="font-size: medium;">$ \Rightarrow {a^3} + {b^3} + {c^3} - 3abc $$= {a^3} + \left( {{b^3} + {c^3}} \right) - 3abc $</span></p> <p><span style="font-size: medium;">$ \Leftrightarrow {a^3} + {b^3} + {c^3} - 3abc= {a^3} + {\left( {b + c} \right)^3} - 3bc\left( {b + c} \right) - 3abc$$ \Leftrightarrow {a^3} + {b^3} + {c^3} - 3abc $$= \left( {a + b + c} \right)\left( {{a^2} - a\left( {b + c} \right) + {{\left( {b + c} \right)}^2}} \right) - \left[ {3bc\left( {b + c} \right) + 3abc} \right]$$ \Leftrightarrow {a^3} + {b^3} + {c^3} - 3abc = \left( {a + b + c} \right)\left( {{a^2} - a\left( {b + c} \right) + {{\left( {b + c} \right)}^2}} \right) - 3bc\left( {a + b + c} \right)$$ \Leftrightarrow {a^3} + {b^3} + {c^3} - 3abc = \left( {a + b + c} \right)\left( {{a^2} - a\left( {b + c} \right) + {{\left( {b + c} \right)}^2} - 3bc} \right)$$ \Leftrightarrow {a^3} + {b^3} + {c^3} - 3abc = \left( {a + b + c} \right)\left( {{a^2} - ab - ac + {b^2} + 2bc + {c^2} - 3bc} \right)$$ \Leftrightarrow {a^3} + {b^3} + {c^3} - 3abc = \left( {a + b + c} \right)\left( {{a^2} + {b^2} + {c^2} - ab - ac - bc} \right)$</span></p> <p><span style="font-size: medium;">Do đó nếu \({a^3} + {b^3} + {c^3} - 3abc = 0\) thì \(a + b + c = 0\) hoặc \({a^2} + {b^2} + {c^2} - ab - bc - ac = 0\)</span></p> <p><span style="font-size: medium;">Mà \({a^2} + {b^2} + {c^2} - ab - bc - ac = \dfrac{1}{2}.\left[ {{{\left( {a - b} \right)}^2} + {{\left( {a - c} \right)}^2} + {{\left( {b - c} \right)}^2}} \right]\) suy ra \(a = b = c\).</span></p> </div> </div> </div> </div></div> <div id="end_sub_question_nav"></div>

Trắc nghiệm Bài tập ôn tập chương 1 Toán 8

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