Question

How do you factor `18x^2-31xy+6y^2`?

Answer 1

`z = 18x^2 - 31yx + 6y^2`= (x - p)(x - q). Use the new AC Method.
Convert z to `z' = x^2 - 31yx + 108y^2` = (x - p')(x - q').
Compose factor pairs of`(108y^2)` -> (2, 54)(3, 36)(4, 27) = -b.
Then, p' = -4y and q' = -27y.

Next, `p = (-4y)/18 = (-2y)/9` and `q = (q')/18 = -(3y)/2.`

Factored form: `z = (x - (2y)/9)(x - (3y)/2) = (9x - 2y)(2x - 3y)`