# How do you factor 4x^2+15x+9?

Jun 22, 2016

$4 {x}^{2} + 15 x + 9 = \left(4 x + 3\right) \left(x + 3\right)$

#### Explanation:

Use an AC method.

Find a pair of factors of $A C = 4 \cdot 9 = 36$ with sum $B = 15$

The pair $12 , 3$ works in that $12 + 3 = 15$ and $12 \times 3 = 36$

Use this pair to split the middle term, then factor by grouping...

$4 {x}^{2} + 15 x + 9$

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

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

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

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