Answer
$2x(x-12)(x-8)$
Work Step by Step
Factoring the $GCF=
2x
$, the given expression, $
2x^3-40x^2+192x
,$ is equivalent to
\begin{array}{l}
2x(x^2-20x+96)
.\end{array}
The 2 numbers whose product is $ac=
1(96)=96
$ and whose sum is $b=
-20
$ are $\left\{
-12,-8
\right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then
\begin{array}{l}
2x(x^2-12x-8x+96)
\\\\=
2x[(x^2-12x)-(8x-96)]
\\\\=
2x[x(x-12)-8(x-12)]
\\\\=
2x[(x-12)(x-8)]
\\\\=
2x(x-12)(x-8)
.\end{array}