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