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

$z = 18 {x}^{2} - 31 y x + 6 {y}^{2}$= (x - p)(x - q). Use the new AC Method.
Convert z to $z ' = {x}^{2} - 31 y x + 108 {y}^{2}$ = (x - p')(x - q').
Compose factor pairs of$\left(108 {y}^{2}\right)$ -> (2, 54)(3, 36)(4, 27) = -b.
Next, $p = \frac{- 4 y}{18} = \frac{- 2 y}{9}$ and $q = \frac{q '}{18} = - \frac{3 y}{2.}$
Factored form: $z = \left(x - \frac{2 y}{9}\right) \left(x - \frac{3 y}{2}\right) = \left(9 x - 2 y\right) \left(2 x - 3 y\right)$