# How do you factor y= 2x^2 - 9x – 18 ?

Dec 30, 2015

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

#### Explanation:

If the factored quadratic is expressed as $\left(a x + b\right) \left(c x + d\right)$ then the general form of a quadratic is $y = a c {x}^{2} + \left(b c + a d\right) x + b d$
We therefore need to look for factors of $2$ and $\left(- 18\right)$ that will combine to give $\left(- 9\right)$
Possible factors of $2$ are only $2$ and $1$
Possible factors of $\left(- 18\right)$ are $- 9$ and $2$ or $- 6$ and $3$
$2 \cdot \left(- 6\right) + 1 \cdot 3 = - 9$ so these are the correct factors.
Hence $y = \left(2 x + 3\right) \left(x - 6\right)$