# How do you factor n^2+2n-15?

##### 2 Answers
May 30, 2015

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like $a {n}^{2} + b n + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = 1 \cdot - 15 = - 15$
AND
${N}_{1} + {N}_{2} = b = 2$

After trying out a few numbers we get ${N}_{1} = 5$ and ${N}_{2} = - 3$
$5 \cdot - 3 = - 15$, and $5 + \left(- 3\right) = 2$

${n}^{2} + 2 n - 15 = {n}^{2} + 5 n - 3 n - 15$

$= n \left(n + 5\right) - 3 \left(n + 5\right)$

$\left(n + 5\right)$ is a common factor to each of the terms

=color(green)((n+5)(n-3)

May 30, 2015

${n}^{2} + 2 n - 15$

By factorization:

n^2+color(red)2ncolor(blue)[-15

working rArr -5+3=color(red)2, -5xx3=color(blue)[-15

${n}^{2} - 5 n + 3 n - 15$

$n \left(n - 5\right) + 3 \left(n - 5\right)$

Answer :
color(green)[(n+3)(n-5)