How do you factor $12 y^{2} - 7 y + 1$ $12y^2-7y+1$ ?

Question

How do you factor $12 y^{2} - 7 y + 1$ $12y^2-7y+1$ ?

1 Answer

Impact of this question

3055 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-11T16:42:25

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

Explanation:

$12 y^{2} - 7 y + 1$ $12y^2−7y+1$

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

In this technique, if we have to factorise an expression like $a y^{2} + b y + c$ $ay^2 + by + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 12 \cdot 1 = 12$ $N_1*N_2 = a*c = 12*1 = 12$
and,
$N_{1} + N_{2} = b = - 7$ $N_1 +N_2 = b = -7$

After trying out a few numbers we get $N_{1} = - 3$ $N_1 = -3$ and $N_{2} = - 4$ $N_2 =-4$
$- 3 \cdot - 4 = 12$ $-3*-4 = 12$ , and $- 3 + (- 4) = - 7$ $-3+(-4)= -7$

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

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

Science

Math

Humanities

... and beyond

How do you factor $12 y^{2} - 7 y + 1$ $12y^2-7y+1$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you factor 12y2−7y+112y^2-7y+1 ?

1 Answer

Explanation:

Related questions

Impact of this question

How do you factor $12 y^{2} - 7 y + 1$ $12y^2-7y+1$ ?