# How do you factor y^2 - 2y - 3 ?

Jun 3, 2015

${y}^{2} - 2 y - 3$

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

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot - 3 = - 3$
and
${N}_{1} + {N}_{2} = b = - 2$

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

${y}^{2} - 2 y - 3 = {y}^{2} - 3 y + y - 3$

${y}^{2} - 3 y + y - 3 = y \left(y - 3\right) + 1 \left(y - 3\right)$

$\left(y - 3\right)$ is a common factor to each of the terms

=color(green)((y+1)(y-3)