# How do you factor 5y^2-3y-2?

Aug 10, 2015

= color(blue)((5y+2)(y-1)

#### Explanation:

5y^2−3y-2

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 5 \cdot - 2 = - 10$
and,
${N}_{1} + {N}_{2} = b = - 3$

After trying out a few numbers we get ${N}_{1} = - 5$ and ${N}_{2} = 2$
$- 5 \cdot 2 = - 10$, and $2 + \left(- 5\right) = - 3$

5y^2−color(blue)(3y)-2 = 5y^2−color(blue)(5y+2y)-2

$= 5 y \left(y - 1\right) + 2 \left(y - 1\right)$

= color(blue)((5y+2)(y-1)