# How do you factor completely: 2x^2-10x+12?

Jul 28, 2015

 color(blue)((2)(x-2)(x-3) is the factorised form.

#### Explanation:

 2x^2−10x+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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 2 \cdot 12 = 24$
and
${N}_{1} + {N}_{2} = b = - 10$

After trying out a few numbers we get ${N}_{1} = - 6$ and ${N}_{2} = - 4$
$\left(- 6\right) \cdot \left(- 4\right) = 24$, and $- 6 + \left(- 4\right) = - 10$

 2x^2−10x+12 = 2x^2−6x -4x+12

$= 2 x \left(x - 3\right) - 4 \left(x - 3\right)$

Here, $\left(x - 3\right)$ is common to both terms:

$= \left(2 x - 4\right) \left(x - 3\right)$
Also, $2$ is common to both terms of the first bracket

 color(blue)(2(x-2)(x-3) is the factorised form.