# How do you factor x^2 + 8x + 12?

Jun 12, 2016

${x}^{2} + 8 x + 12 = \textcolor{g r e e n}{\left(x + 2\right) \left(x + 6\right)}$

#### Explanation:

In general
$\textcolor{w h i t e}{\text{XXX}} \left({x}^{2} + \left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right) x + \textcolor{red}{a} \cdot \textcolor{b l u e}{b}\right) = \left(x + \textcolor{red}{a}\right) \left(x + \textcolor{b l u e}{b}\right)$

$8 = \textcolor{red}{2} + \textcolor{b l u e}{6}$
and
$12 = \textcolor{red}{2} \cdot \textcolor{b l u e}{6}$

So
${x}^{2} + 8 x + 12$

color(white)("XXX")=(x^2+(color(red)(2)+color(blue)(6))x+color(red)(2)*color(blue)(6)

$\textcolor{w h i t e}{\text{XXX}} = \left(x + \textcolor{red}{2}\right) \left(x + \textcolor{b l u e}{6}\right)$