# How do you factor  x^2 - 9x + 14 ?

May 24, 2015

${x}^{2} - 9 x + 14$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 14 = 14$
and
${N}_{1} + {N}_{2} = b = - 9$

After trying out a few numbers we get ${N}_{1} = - 2$ and ${N}_{2} = - 7$
$\left(- 2\right) . \left(- 7\right) = 14$, and $\left(- 2\right) + \left(- 7\right) = - 9$

${x}^{2} - 9 x + 14 = {x}^{2} - 7 x - 2 x + 14$

$= x \left(x - 7\right) - 2 \left(x - 7\right)$

=color(green)((x-7)(x-2)