# How do you factor 3y^2 +13y + 4?

Feb 26, 2016

color(blue)((3y+1) (y+4)  is the factorised form of the equation.

#### Explanation:

$3 {y}^{2} + 13 y + 4$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 3 \cdot 4 = 12$

AND

${N}_{1} + {N}_{2} = b = 13$

After trying out a few numbers we get ${N}_{1} = 12$ and ${N}_{2} = 1$
$12 \cdot 1 = 12$, and $12 + 1 = 13$

$3 {y}^{2} + 13 y + 4 = 3 {y}^{2} + 12 y + y + 4$

$= 3 y \left(y + 4\right) + 1 \left(y + 4\right)$

$\left(y + 4\right)$ is a common factor to each of the terms.
$= \left(3 y + 1\right) \left(y + 4\right)$

color(blue)((3y+1) (y+4)  is the factorised form of the equation.