# How do you factor 5p^2 - p - 6 ?

May 30, 2015

$5 {p}^{2} - p - 6$

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like $a {p}^{2} + b p + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 5 \cdot \left(- 6\right) = - 30$
and
${N}_{1} + {N}_{2} = b = - 1$

After trying out a few numbers we get ${N}_{1} = - 6$ and ${N}_{2} = 5$
$- 6 \cdot \left(5\right) = - 30$, and $5 + \left(- 6\right) = - 1$

$5 {p}^{2} - p - 6 = 5 {p}^{2} + 5 p - 6 p - 6$

$= 5 p \left(p + 1\right) - 6 \left(p + 1\right)$

 =color(blue)((5p - 6)(p+1)