# How do you factor the expression 4a ^3 + 15a ^2 - 4a?

Feb 3, 2016

$4 {a}^{3} + 15 {a}^{2} - 4 a = \textcolor{g r e e n}{a \left(4 a - 1\right) \left(a + 4\right)}$

#### Explanation:

First remove the obvious common factor of $\textcolor{red}{a}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} \left(\textcolor{b l u e}{4} {a}^{2} + \textcolor{\mathmr{and} a n \ge}{15} a \textcolor{c y a n}{- 4}\right)$

check for factors of $\textcolor{b l u e}{4}$ which when cross multiplied by factors of $\textcolor{c y a n}{- 4}$ have a sum of $\textcolor{\mathmr{and} a n \ge}{15}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} \left(\textcolor{p u r p \le}{4 a - 1}\right) \left(\textcolor{b r o w n}{a + 4}\right)$