Answer
$4(2x+1)(x-5)$
Work Step by Step
$8x^{2}-36x-20$
...factor out the GCF.
$=4(2x^{2}-9x-5)$
...factor $(2x^{2}-9x-5)$.
$ac=-10,\ b=-9$, find factors of $-10$ with a sum of $-9$.
$\left[\begin{array}{lllll}
\text{Factors of -10 } & \text{Sum of factors} & & & \\
1\text{ and }-10 & -9 & \text{...what we need}\\
2\text{ and }-5 & -3 & & & \\
-2\text{ and }5 & 3 & & &
\end{array}\right]$
$4(2x^{2}-9x-5)$
...use the found factors to rewrite $bx$.
$=4(2x^{2}+x-10x-5)$
...factor out the GCF.
$=4[x(2x+1)-5(2x+1)]$
...use the Distributive Property to finish factoring.
$=4(2x+1)(x-5)$
