# How do you factor 12r^2 - 7r - 12 by grouping?

Aug 18, 2016

$12 {r}^{2} - 7 r - 12 = \left(4 r - 3\right) \left(3 r - 4\right)$

#### Explanation:

We need to find how to split the middle term. To do that, use an AC method:

Look for a pair of factors of $A C = 12 \cdot 12 = 144$ which differ by $B = 7$

The pair $16 , 9$ works, so we find:

$12 {r}^{2} - 7 r - 12$

$= 12 {r}^{2} - 16 r + 9 r - 12$

$= \left(12 {r}^{2} - 16 r\right) + \left(9 r - 12\right)$

$= 4 r \left(3 r - 4\right) + 3 \left(3 r - 4\right)$

$= \left(4 r - 3\right) \left(3 r - 4\right)$