Answer
$2r(r-4)(r+8)$
Work Step by Step
Factoring the $GCF=
2r
,$ the given expression, $
2r^3+8r^2-64r
,$ is equivalent to
\begin{array}{l}\require{cancel}
2r(r^2+4r-32)
.\end{array}
The trinomial expression above has $c=
-32
$ and $b=
4
.$
The possible factors of $c$ are $
\{ 1,-32 \}
,\{ 2,-16 \}
,\{ 4,-8 \}
\{ -1,32 \}
,\{ -2,16 \}
,\{ -4,8 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-4,8
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
2r(r-4)(r+8)
.\end{array}