Answer
$z(2x-3)(x+4)$
Work Step by Step
Factoring the $GCF=z$ of the given expression, $
2x^2z+5xz-12z
$, results to
\begin{array}{l}\require{cancel}
z(2x^2+5x-12)
.\end{array}
The two numbers whose product is $ac=
2(-12)=-24
$ and whose sum is $b=
5
$ are $\{
-3,8
\}$. Using these two numbers to decompose the middle term, then the factored form of the resulting expression, $
z(2x^2+5x-12)
$,is
\begin{array}{l}\require{cancel}
z(2x^2-3x+8x-12)
\\\\=
z[(2x^2-3x)+(8x-12)]
\\\\=
z[x(2x-3)+4(2x-3)]
\\\\=
z[(2x-3)(x+4)]
\\\\=
z(2x-3)(x+4)
.\end{array}
