# How do you factor 18x^2 -15x - 18?

Feb 12, 2017

$18 {x}^{2} - 15 x - 18 = 3 \left(3 x + 2\right) \left(2 x - 3\right)$

#### Explanation:

First separate out the common scalar factor $3$, then use an AC method...

$18 {x}^{2} - 15 x - 18 = 3 \left(6 {x}^{2} - 5 x - 6\right)$

To factor $6 {x}^{2} - 5 x - 6$ first look for a pair of factors of $A C = 6 \cdot 6 = 36$ which differ by $B = 5$.

The pair $9 , 4$ works.

Use this pair to split the middle term and factor by grouping:

$6 {x}^{2} - 5 x - 6 = \left(6 {x}^{2} - 9 x\right) + \left(4 x - 6\right)$

$\textcolor{w h i t e}{6 {x}^{2} - 5 x - 6} = 3 x \left(2 x - 3\right) + 2 \left(2 x - 3\right)$

$\textcolor{w h i t e}{6 {x}^{2} - 5 x - 6} = \left(3 x + 2\right) \left(2 x - 3\right)$

Putting it all together:

$18 {x}^{2} - 15 x - 18 = 3 \left(3 x + 2\right) \left(2 x - 3\right)$