# How do you factor y=x^3 + 8x^2 + 19x + 12 ?

Jun 15, 2016

$\left(x + 1\right) \left(x + 4\right) \left(x - 3\right)$

#### Explanation:

First, use all integer negative numbers that divide the known term 12 and substitute them in x
Prove x=-1
$y = {\left(- 1\right)}^{3} + 8 \cdot {\left(- 1\right)}^{2} + 19 \cdot \left(- 1\right) + 12 = 0$
then use Ruffini method to have:

$\left({x}^{2} + 7 x + 12\right) \left(x + 1\right)$

$x = \frac{- 7 \pm \sqrt{49 - 48}}{2}$
$x = \frac{- 7 \pm 1}{2}$
$x = - 4 \mathmr{and} x = 3$