# How do you factor x^2-5x+6=0?

Apr 30, 2016

color(green)((x-3)(x-2) is the factorised form of the expression.

#### Explanation:

${x}^{2} - 5 x + 6 = 0$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 6 = 6$

AND

${N}_{1} + {N}_{2} = b = - 5$

After trying out a few numbers we get ${N}_{1} = - 2$ and ${N}_{2} = - 3$

$\left(- 2\right) \cdot \left(- 3\right) = 6$, and $\left(- 2\right) + \left(- 3\right) = - 5$

${x}^{2} - 5 x + 6 = {x}^{2} - 2 x - 3 x + 6$

$= x \left(x - 2\right) - 3 \left(x - 2\right)$

$\left(x - 2\right)$ is a common factor to each of the terms

=color(green)((x-3)(x-2)