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