Answer
$3w^2(w+3)(w+15)$
Work Step by Step
Factoring the $GCF=
3w^2
,$ the given expression, $
3w^4+54w^3+135w^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
3w^2(w^2+18w+45)
.\end{array}
The trinomial expression above has $c=
45
$ and $b=
18
.$
The possible factors of $c$ are $
\{ 1,45 \}
,\{ 3,15 \}
,\{ 5,9 \}
,\{ -1,-45 \}
,\{ -3,-15 \}
,\{ -5,-9 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
3,15
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
3w^2(w+3)(w+15)
.\end{array}
