# How do you write 4x^2+2x-12 in factored form?

Sep 16, 2015

$4 {x}^{2} + 2 x - 12$
$\textcolor{w h i t e}{\text{XXXXXX}} = \textcolor{g r e e n}{2} \textcolor{red}{\left(2 x + 3\right)} \textcolor{b l u e}{\left(x - 2\right)}$

#### Explanation:

Extract the obvious constant factor of $2$ to simplify

$\textcolor{g r e e n}{2} \textcolor{\mathmr{and} a n \ge}{\left(2 {x}^{2} + x - 6\right)}$

Factoring
by looking for integer factors $a$ and $b$ of $2$
and integer factors $c$ and $d$ of $\left(- 6\right)$
such that
$\left(a d + b c\right) x = 1 x$

The only integer factors of $2$ are $1 \times 2$

Integer factors of $\left(- 6\right)$ are $\left\{\left(1 \times - 6\right) , \left(2 \times - 3\right) \left(- 1 \times 6\right) , \left(- 3 \times 2\right)\right\}$

Checking the four possible combinations, we find:
$\textcolor{\mathmr{and} a n \ge}{\left(2 {x}^{2} + x - 6\right)} = \textcolor{red}{\left(2 x + 3\right)} \textcolor{b l u e}{\left(x - 2\right)}$

So $4 {x}^{2} + 2 x - 12$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{g r e e n}{2} \textcolor{\mathmr{and} a n \ge}{\left(2 {x}^{2} + x - 6\right)}$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{g r e e n}{2} \textcolor{red}{\left(2 x + 3\right)} \textcolor{b l u e}{\left(x - 2\right)}$