Answer
$2w^2(w+3)(w-16)$
Work Step by Step
Factoring the $GCF=
2w^2
,$ the given expression, $
2w^4-26w^3-96w^2
,$ is equivalent to
\begin{array}{l}\require{cancel}
2w^2(w^2-13w-48)
.\end{array}
The trinomial expression above has $c=
-48
$ and $b=
-13
.$
The possible factors of $c$ are $
\{ 1,-48 \}
,\{ 2,-24 \}
,\{ 3,-16 \}
,\{ 4,-12 \}
,\{ 6,-8 \}
,\{ -1,48 \}
,\{ -2,24 \}
,\{ -3,16 \}
,\{ -4,12 \}
,\{ -6,8 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
3,-16
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
2w^2(w+3)(w-16)
.\end{array}
