# How do you factor completely 15x^2 + 7x - 2?

Aug 28, 2016

$15 {x}^{2} + 7 x - 2 = \left(5 x - 1\right) \left(3 x + 2\right)$

#### Explanation:

Given:

$15 {x}^{2} + 7 x - 2$

Use an AC method: Find a pair of factors of $A C = 15 \cdot 2 = 30$ which differ by $B = 7$.

The pair $10 , 3$ works.

Use this pair to split the middle term then factor by grouping as follows:

$15 {x}^{2} + 7 x - 2$

$= 15 {x}^{2} + 10 x - 3 x - 2$

$= \left(15 {x}^{2} + 10 x\right) - \left(3 x + 2\right)$

$= 5 x \left(3 x + 2\right) - 1 \left(3 x - 2\right)$

$= \left(5 x - 1\right) \left(3 x + 2\right)$