Question

How do you factor the trinomial `12y^2-13y+3`?

Answer 1

`12y^2-13y+3 = (3y-1)(4y-3)`

Explanation:

Given:

`12y^2-13y+3`

Use an AC method:

Look for a pair of factors of `AC = 12*3 = 36` with sum `B=13`

The pair `9, 4` works.

Use this pair to split the middle term, then factor by grouping:

`12y^2-13y+3 = 12y^2-9y-4y+3`

`color(white)(12y^2-13y+3) = (12y^2-9y)-(4y-3)`

`color(white)(12y^2-13y+3) = 3y(4y-3)-1(4y-3)`

`color(white)(12y^2-13y+3) = (3y-1)(4y-3)`