Question

Solve:
$49(x^4-5x^3-24x^2)÷11x(x-8)$

Answer 1

We have, $x^4-5x^3-24x^2$

$=x^2(x^2-5x-24)$

$=x^2[x^2-8x+3x-24]$

$=x^2\left[x\right(x-8)+3(x-8\left)\right]$

$=x^2(x-8)(x+3)$

Therefore,

$49(x^4-5x^3-24x^2)÷11x(x-8)$

$=\frac{49(x^4-5x^3-24x^2)}{11x(x-8)}$

$=\frac{49x^2(x-8)(x+3)}{11x(x-8)}$

$=\frac{49x(x+3)}{11}$

Hence, $49(x^4-5x^3-24x^2)÷11x(x-8)=\frac{49x(x+3)}{11}$