# How do you factor 4y² -13y -12?

##### 1 Answer
May 30, 2015

Use a version of the AC Method.

$A = 4$, $B = 13$, $C = 12$

Look for a pair of factors of $A C = 48$ whose difference is $B = 13$.

$16$ and $3$ work.

Use this pair to split the middle term then factor by grouping...

$4 {y}^{2} - 13 y - 12$

$= 4 {y}^{2} + 3 y - 16 y - 12$

$= \left(4 {y}^{2} + 3 y\right) - \left(16 y + 12\right)$

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

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