Answer
$4x(x-2)(5x+9)$
Work Step by Step
Factoring the $GCF=
4x
$, then the given expression, $
20x^3-4x^2-72x
$ is equivalent to
\begin{array}{l}
4x(5x^2-x-18)
.\end{array}
The two numbers whose product is $ac=
5(-18)=-90
$ and whose sum is $b=
-1
$ are $\{
-10,9
\}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is
\begin{array}{l}
4x(5x^2-10x+9x-18)
\\\\=
4x[(5x^2-10x)+(9x-18)]
\\\\=
4x[5x(x-2)+9(x-2)]
\\\\=
4x[(x-2)(5x+9)]
\\\\=
4x(x-2)(5x+9)
.\end{array}
