# How do you factor 12y^2-7y+1 ?

Aug 11, 2015

color(blue)((3y-1)(4y-1)  is the factorised form of the expression.

#### Explanation:

12y^2−7y+1

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 12 \cdot 1 = 12$
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 $- 3 + \left(- 4\right) = - 7$

12y^2−color(blue)(7y)+1 =12y^2−color(blue)(3y -4y)+1

$= 3 y \left(4 y - 1\right) - 1 \left(4 y - 1\right)$
color(blue)((3y-1)(4y-1)  is the factorised form of the expression.