# How do you write x^2+8x+12 in factored form?

Sep 16, 2015

color(blue)((x+2)(x+6) is the factorised

#### Explanation:

${x}^{2} + 8 x + 12$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 2 \cdot 6 = 12$
and
${N}_{1} + {N}_{2} = b = 8$

After trying out a few numbers we get ${N}_{1} = 2$ and ${N}_{2} = 6$
$2 \cdot 6 = 12$ and $2 + 6 = 8$

${x}^{2} + 8 x + 12 = {x}^{2} + 6 x + 2 x + 12$

$= x \left(x + 6\right) + 2 \left(x + 6\right)$

color(blue)((x+2)(x+6) is the factorised form of the exam.