# How do you factor 2x^2-5x-12 ?

##### 1 Answer
Aug 5, 2015

=color(green)((2x+3)(x-4)

#### Explanation:

2x^2−5x−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,
${N}_{1} + {N}_{2} = b = - 5$

After trying out a few numbers we get:
${N}_{1} = - 8$ and ${N}_{2} = 3$
$3 \cdot \left(- 8\right) = - 24$, and
$3 + \left(- 8\right) = - 5$

2x^2−color(blue)(5x)−12 = 2x^2−color(blue)(8x +3x)−12

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

$\left(x - 4\right)$ is a common factor to each of the terms

=color(green)((2x+3)(x-4)