# How do you factor 12x^2 - 5x - 2 by grouping?

Jun 12, 2016

$\left(3 x - 2\right) \left(4 x + 1\right)$

#### Explanation:

First multiply $12 \times 2 = 24$
Find factors of 24 which differ by 5. These are 8 and 3.

This tells you how to rewrite the middle term (-5)

$12 {x}^{2} - 8 x + 3 x - 2$

$\left(12 {x}^{2} - 8 x\right) + \left(3 x - 2\right) \text{ form pairs}$

$4 x \left(3 x - 2\right) + \left(3 x - 2\right) \text{ common factor}$

$\left(3 x - 2\right) \left(4 x + 1\right) \text{ common bracket}$