# How do you factor completely 6x^2 + x - 15?

Mar 11, 2016

$6 {x}^{2} + x - 15 = \left(3 x + 5\right) \left(2 x - 3\right)$

#### Explanation:

Use an AC method: Look for two factors of $A C = 6 \cdot 15 = 90$ which differ by $B = 1$.

The pair $9 , 10$ works.

Then use that pair to split the middle term and factor by grouping:

$6 {x}^{2} + x - 15$

$= 6 {x}^{2} - 9 x + 10 x - 15$

$= \left(6 {x}^{2} - 9 x\right) + \left(10 x - 15\right)$

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

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