Answer
$x(x-2)(x+10)$
Work Step by Step
For the polynomial $x^3 + 8x^2 - 20x=x(x^2 +8x - 20)$ we have to find integers whose product is $-20$ and whose sum is $8$. That is, we have $-2$ and $10$, where $-2+10=8$ and $-2\times (10)=-20$. Thus
$$
x(x^2 +8x - 20)=x(x-2)(x+10)
.$$