Answer
$4(x+9)(x-4)$
Work Step by Step
Factoring the $GCF=
4
$, then the given expression, $
4x^2+20x-144
$ is equivalent to
\begin{array}{l}
4(x^2+5x-36)
.\end{array}
The two numbers whose product is $ac=
1(-36)=-36
$ and whose sum is $b=
5
$ are $\{
9,-4
\}$. Using these two numbers to decompose the middle term of the trinomial above, then the complete factored form is
\begin{array}{l}
4(x^2+9x-4x-36)
\\\\=
4[(x^2+9x)-(4x+36)]
\\\\=
4[x(x+9)-4(x+9)]
\\\\=
4[(x+9)(x-4)]
\\\\=
4(x+9)(x-4)
.\end{array}
