Question

Factorize -2x^3+22x^2+24x

Answer 1

the answer will be -1 and 12

Answer 2

The expression is $-2x^3+22x+24x$. Factoring we have

$-2x^3+22x+24x=-2x(x^2-11x-12)$.

Now finds the roots of the equation $x^2-11x-12=0\\ x=\frac{11 \pm \sqrt{11^2+48}}{2} \\ x=\frac{11 \pm \sqrt{169}}{2} \\ x=\frac{11 \pm 13}{2} \\ x=12,-1$

Thus $x^2-11x-12=(x-12)(x+1)$

The factored form is

$-2x^3+22x+24x=-2x(x-12)(x+1)$