Answer
$x(x+10)(x-2)$
Work Step by Step
Factor out $x$.
$x^3+8x^2-20x=x(x^2+8x-20)$
Look for factors of $-20$ whose sum is equal to the middle term's coeffient $(8)$. The factors are $10$ and $-2$.
Use the factors found to rewrite the middle term $8x$ as $10x-2x$.
$=x(x^2+10x-2x-20)$
Group the first two terms together and group the last two terms together to obtain:
$=x[(x^2+10x)+(-2x-20)]$
Factor out the GCF in each group.
$=x[x(x+10)+(-2)(x+10)]$
$=x[x(x+10)-2(x+10)]$
Factor out $(x+10)$.
$=x(x+10)(x-2)$
Hence, the completely factored form of the given expression is $x(x+10)(x-2)$.
