# How do you factor 5a^2 - 5a - 100?

Jun 4, 2015

Extract the obvious numeric factor of $5$ from $5 {a}^{2} - 5 a - 100$ to get
$\textcolor{w h i t e}{\text{XXXX}}$$5 \left({a}^{2} - 1 a - 20\right)$

So we are looking for two numbers, $p$ and $q$
such that
$\textcolor{w h i t e}{\text{XXXX}}$$p + q = - 1$
and
$\textcolor{w h i t e}{\text{XXXX}}$$p \cdot q = - 20$

With only a little consideration of the options, we get
$\textcolor{w h i t e}{\text{XXXX}}$$\left(4 , - 5\right)$
and the final factors are
$\textcolor{w h i t e}{\text{XXXX}}$$= 5 \left(a + 4\right) \left(a - 5\right)$