Answer
$3r(r+3)(r-6)$
Work Step by Step
Factoring the $GCF=
3r
,$ the given expression, $
3r^3-9r^2-54r
,$ is equivalent to
\begin{array}{l}\require{cancel}
3r(r^2-3r-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}
3r(r+3)(r-6)
.\end{array}
