How do you factor 12y^2-7y+1 12y2−7y+1?

1 Answer
Don't Memorise
Aug 11, 2015

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

Explanation:

12y^2−7y+1 12y2−7y+1

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like ay^2 + by + cay2+by+c, we need to think of 2 numbers such that:

N_1*N_2 = a*c = 12*1 = 12N1⋅N2=a⋅c=12⋅1=12
and,
N_1 +N_2 = b = -7N1+N2=b=−7

After trying out a few numbers we get N_1 = -3N1=−3 and N_2 =-4N2=−4
-3*-4 = 12−3⋅−4=12, and -3+(-4)= -7−3+(−4)=−7

12y^2−color(blue)(7y)+1 =12y^2−color(blue)(3y -4y)+1 12y2−7y+1=12y2−3y−4y+1

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

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