Answer
$2(x-3)(x+8)$
Work Step by Step
Factoring the $GCF=
2
,$ the given expression, $
2x^2+10x-48
,$ is equivalent to
\begin{array}{l}\require{cancel}
2(x^2+5x-24)
.\end{array}
The trinomial expression above has $c=
-24
$ and $b=
5
.$
The possible factors of $c$ are $
\{ 1,-24 \}
,\{ 2,-12 \}
,\{ 3,-8 \}
,\{ 4,-6 \}
,\{ -1,24 \}
,\{ -2,12 \}
,\{ -3,8 \}
,\{ -4,6 \}
$. Among these factors, the pair whose sum is equal to $b$ is $\{
-3,8
\}.$ Hence, the factored form of the given expression is
\begin{array}{l}\require{cancel}
2(x-3)(x+8)
.\end{array}