# How do you factor 3y^2 -21y+36?

Aug 11, 2015

color(green)((3y-9)(y-4)  is the factorised form of the expression.

#### Explanation:

3y^2−21y+36

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 3 \cdot 36 = 108$

and,

${N}_{1} + {N}_{2} = b = - 21$

After trying out a few numbers we get ${N}_{1} = - 12$ and ${N}_{2} = - 9$

$\left(- 12\right) \cdot \left(- 9\right) = 108$, and $\left(- 12\right) + \left(- 9\right) = - 21$

3y^2−color(green)(21y)+36 = 3y^2color(green)(-12y-9y)+36

$= 3 y \left(y - 4\right) - 9 \left(y - 4\right)$

color(green)((3y-9)(y-4)  is the factorised form of the expression.