# How do you factor 18x^2+3x-10 by grouping?

May 11, 2016

$18 {x}^{2} + 3 x - 10 = \left(3 x - 2\right) \left(6 x + 5\right)$

#### Explanation:

You need to find how to split the middle term first.

Use an AC Method:

Look for a pair of factors of $A C = 18 \cdot 10 = 180$ which differ by $B = 3$.

The pair $15 , 12$ works in that $15 \times 12 = 180$ and $15 - 12 = 3$.

Use this pair to split the middle term and factor by grouping:

$18 {x}^{2} + 3 x - 10$

$= 18 {x}^{2} + 15 x - 12 x - 10$

$= \left(18 {x}^{2} + 15 x\right) - \left(12 x + 10\right)$

$= 3 x \left(6 x + 5\right) - 2 \left(6 x + 5\right)$

$= \left(3 x - 2\right) \left(6 x + 5\right)$