# How do you factor x^2 - 2x - 8?

Jun 10, 2015

color(blue)((x+2)(x - 4)

#### Explanation:

${x}^{2} - 2 x - 8$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 8\right) = - 8$
and
${N}_{1} + {N}_{2} = b = - 2$

After trying out a few numbers we get ${N}_{1} = - 4$ and ${N}_{2} = 2$
$- 4 \cdot 2 = - 8$, and $2 + \left(- 4\right) = - 2$

${x}^{2} - 2 x - 8 = {x}^{2} - 4 x + 2 x - 8$
$= x \left(x - 4\right) + 2 \left(x - 4\right)$
=color(blue)((x+2)(x - 4)