# How do you factor x^2 +3x - 18 = 0?

May 23, 2015

${x}^{2} + 3 x - 18$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 18\right) = - 18$
and,
${N}_{1} + {N}_{2} = b = 3$

After trying out a few numbers we get ${N}_{1} = 6$ and ${N}_{2} = - 3$
$6 \cdot \left(- 3\right) = - 18$ and $6 + \left(- 3\right) = 3$

${x}^{2} + 3 x - 18 = {x}^{2} + 6 x - 3 x - 18$

$x \left(x + 6\right) - 3 \left(x + 6\right)$

color(green)((x-3)color(red)((x + 6) is the factorised form.