# How do you factor 12+ 16x - 3x ^ { 2}?

Jun 15, 2017

$= \left(6 - x\right) \left(2 + 3 x\right)$

#### Explanation:

$12 + 16 x - 3 {x}^{2}$

$= 12 - 2 x + 18 x - 3 {x}^{2}$

$= 2 \left(6 - x\right) + 3 x \left(6 - x\right)$

$= \left(6 - x\right) \left(2 + 3 x\right)$

Jun 15, 2017

The equation can be factorised to $\left(- 3 x - 2\right) \left(x - 6\right)$

#### Explanation:

Use the general formula
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Substitute in the given values
$x = \frac{- 16 \pm \sqrt{{16}^{2} - 4 \cdot - 3 \cdot 12}}{- 6}$

simplify
$x = \frac{- 16 \pm 20}{- 6}$

${x}_{\text{1}} = 6$
${x}_{\text{2}} = - \frac{2}{3}$

Put those values back into $a \left(x - {x}_{\text{1")(x-x_"2}}\right)$

gives

$- 3 \left(x + \frac{2}{3}\right) \left(x - 6\right)$

rearranging
$\left(- 3 x - 2\right) \left(x - 6\right)$