# How do you factor 2x^2+5x+2?

Jun 2, 2015

$2 {x}^{2} + 5 x + 2$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:
${N}_{1} \cdot {N}_{2} = 2 \cdot 2 = 4$
and
${N}_{1} + {N}_{2} = b = 5$
After trying out a few numbers we get ${N}_{1} = 4$ and ${N}_{2} = 1$
$4.1 = 4$, and $4 + 1 = 5$

$2 {x}^{2} + 5 x + 2 = 2 {x}^{2} + 4 x + 1 x + 2$
$2 x \left(x + 2\right) + 1 \left(x + 2\right)$

$\left(x + 2\right)$ is common to both the terms.

color(blue)(( 2x+1)(x+2) is the factorised form.