# How do you factor 2y^2+7y+6?

May 30, 2015

$2 {y}^{2} + 7 y + 6$

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 2.6 = 12$
and
${N}_{1} + {N}_{2} = b = 7$
After trying out a few numbers we get ${N}_{1} = 3$ and ${N}_{2} = 4$
$3 \cdot 4 = 12$, and $3 + 4 = 7$

$2 {y}^{2} + 7 y + 6 = 2 {y}^{2} + 4 y + 3 y + 6$
$= 2 {y}^{2} + 4 y + 3 y + 6$
$= 2 y \left(y + 2\right) + 3 \left(y + 2\right)$
 =color(green)((2y+3)(y+2)