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

Aug 8, 2015

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

#### Explanation:

The idea is to break down the middle term into two monomials which can be used in the factorisation process. Note that $2 \cdot 4 = 8 = 8 \cdot 1$, and that we may write $9 = 8 + 1$, which may help us in the process.

Let us write:
$2 {x}^{2} + 9 x + 4$
$= 2 {x}^{2} + 8 x + x + 4$
$= 2 x \left(x + 4\right) + \left(x + 4\right)$
$= \left(2 x + 1\right) \left(x + 4\right)$