Answer
$-x(x-8)(x+2)$
Work Step by Step
Factoring the negative $GCF=
-x
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-x^3+6x^2+16x
\\\\=
-x(x^2-6x-16)
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-x(x^2-6x-16)
\end{array} has $c=
-16
$ and $b=
-6
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-8,2
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
-x(x-8)(x+2)
.\end{array}