# How do you factor 15x^2 - 5x - 10?

Jan 5, 2016

 =color(blue)( (15x+10)(x-1)

#### Explanation:

$15 {x}^{2} - 5 x - 10$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 15 \cdot - 10 = - 150$
AND
${N}_{1} + {N}_{2} = b = - 5$

After trying out a few numbers we get ${N}_{1} = - 15$ and ${N}_{2} = 10$
$10 \cdot - 15 = - 150$, and $10 + \left(- 15\right) = - 5$

$15 {x}^{2} - 5 x - 10 = 15 {x}^{2} - 15 x + 10 x - 10$

$= 15 x \left(x - 1\right) + 10 \left(x - 1\right)$

$\left(x - 1\right)$ is a common factor to each of the terms

 =color(blue)( (15x+10)(x-1)