# How do you factor 5x^2+15x+10?

Jun 2, 2015

$5 {x}^{2} + 15 x + 10$

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:
${N}_{1} \cdot {N}_{2} = a \cdot c = 5 \cdot 10 = 50$
and,
${N}_{1} + {N}_{2} = b = 15$

After trying out a few numbers we get ${N}_{1} = 10$ and ${N}_{2} = 5$
$10 \cdot 5 = 50$, and $10 + 5 = 15$

$5 {x}^{2} + 15 x + 10 = 5 {x}^{2} + 10 x + 5 x + 10$

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

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

 color(green)((5x+5)(x+2) , is the factorised form.