# How do you factor 4x^2+2x-20?

Aug 11, 2015

color(blue)((2x-4)(2x+5)  is the factorised form of the expression.

#### Explanation:

4x^2+2x−20

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 4 \cdot - 20 = - 80$
and
${N}_{1} + {N}_{2} = b = 2$

After trying out a few numbers we get ${N}_{1} = 10$ and ${N}_{2} = - 8$
$10 \cdot \left(- 8\right) = - 80$, and $10 + \left(- 8\right) = 2$

4x^2+color(blue)(2x)−20 =4x^2+color(blue)(10x -8x)−20

$= 2 x \left(2 x + 5\right) - 4 \left(2 x + 5\right)$
color(blue)((2x-4)(2x+5)  is the factorised form for the expression.