Đáp án:
a) $A = 3x$
b)$A= 2{x^2} + 5x + 3$
c) $A= 4{x^2} + x - 3$
d) $A= 2{x^2} + 5x + 2$
Giải thích các bước giải:
\(\begin{array}{l}
a)\,A.\left( {4{x^2} - 1} \right) = \left( {6{x^2} + 3x} \right)\left( {2x - 1} \right)\\
A.\left( {2x + 1} \right)\left( {2x - 1} \right) = 3x\left( {2x + 1} \right)\left( {2x - 1} \right)\\
\Rightarrow A = 3x\\
b)\,A.\left( {4x - 7} \right) = \left( {2x + 3} \right)\left( {4{x^2} - 3x - 7} \right)\\
A.\left( {4x - 7} \right) = \left( {2x + 3} \right)\left( {4{x^2} - 7x + 4x - 7} \right)\\
A.\left( {4x - 7} \right) = \left( {2x + 3} \right)\left( {4x - 7} \right)\left( {x + 1} \right)\\
\Rightarrow A = \left( {2x + 3} \right)\left( {x + 1} \right) = 2{x^2} + 5x + 3\\
c)\,A.\left( {{x^2} - 1} \right) = \left( {4{x^2} - 7x + 3} \right)\left( {{x^2} + 2x + 1} \right)\\
A\left( {{x^2} - 1} \right) = \left( {x - 1} \right)\left( {4x - 3} \right){\left( {x + 1} \right)^2}\\
A\left( {x - 1} \right)\left( {x + 1} \right) = \left( {x - 1} \right)\left( {x + 1} \right)\left( {4x - 3} \right)\left( {x + 1} \right)\\
A = \left( {4x - 3} \right)\left( {x + 1} \right) = 4{x^2} + x - 3\\
d)\,A.\left( {{x^2} - 2x} \right) = \left( {{x^2} + 2x} \right)\left( {2{x^2} - 3x - 2} \right)\\
A\left( {x - 2} \right)x = x\left( {x + 2} \right)\left( {2x + 1} \right)\left( {x - 2} \right)\\
A = \left( {x + 2} \right)\left( {2x + 1} \right) = 2{x^2} + 5x + 2
\end{array}\)
