# How do you factor 3x^2 + 5x - 12?

May 30, 2015

Use a version of the AC Method.

$A = 3$, $B = 5$, $C = 12$

Since the sign on the constant term is $-$, look for a pair of factors of $A C = 36$ whose difference is $B = 5$

The pair $4$, $9$ works.

Now use that pair to split the middle term, then factor by grouping:

$3 {x}^{2} + 5 x - 12$

$= 3 {x}^{2} - 4 x + 9 x - 12$

$= \left(3 {x}^{2} - 4 x\right) + \left(9 x - 12\right)$

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

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