Lời giải

Đáp án đúng là: A

Theo đề ra ta có: $3{x^3} - 8{x^2} - 41x + 30$

$= 3{x^3} - 2{x^2} - 6{x^2} + 4x - 45x + 30$

$= \left( {3{x^3} - 2{x^2}} \right) - \left( {6{x^2} - 4x} \right) - \left( {45x - 30} \right)$

$= {x^2}\left( {3x - 2} \right) - 2x\left( {3x - 2} \right) - 15\left( {3x - 2} \right)$

$= \left( {{x^2} - 2x - 15} \right)\left( {3x - 2} \right)$

$= \left( {{x^2} + 3x - 5x - 15} \right)\left( {3x - 2} \right)$

$= \left[ {\left( {{x^2} + 3x} \right) - \left( {5x + 15} \right)} \right]\left( {3x - 2} \right)$

$= \left[ {x\left( {x + 3} \right) - 5\left( {x + 3} \right)} \right]\left( {3x - 2} \right)$

$= \left( {3x - 2} \right)\left( {x - 5} \right)\left( {x + 3} \right)$