Answer
$4x(x-3)(x+6)$
Work Step by Step
Factoring the $GCF=
4x
,$ the given expression, $
4x^3+12x^2-72x
,$ is equivalent to
\begin{array}{l}\require{cancel}
4x(x^2+3x-18)
.\end{array}
The trinomial expression above has $c=
-18
$ and $b=
3
.$
The possible factors of $c$ are $
\{ 1,-18 \}
,\{ 2,-9 \}
,\{ 3,-6 \}
,\{ -1,18 \}
,\{ -2,9 \}
,\{ -3,6 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-3,6
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
4x(x-3)(x+6)
.\end{array}