Answer
$2r(r+1)(r+3)$
Work Step by Step
Factoring the $GCF=
2r
,$ the given expression, $
2r^3+8r^2+6r
,$ is equivalent to
\begin{array}{l}\require{cancel}
2r(r^2+4r+3)
.\end{array}
The trinomial expression above has $c=
3
$ and $b=
4
.$
The possible factors of $c$ are $
\{ 1,3 \}
,\{ -1,-3 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
1,3
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
2r(r+1)(r+3)
.\end{array}
