# How do you factor 5x^(2) - 7xy - 6y^(2)?

Apr 9, 2016

(5x + 3y)(x - 2y)

#### Explanation:

f(x,y) = 5x^2 - 7xy - 6y^2.= 5(x + p)(x + q)
To factor this trinomial, consider x as variable and y as a constant.
Use the new AC Method (Socratic Search)
Converted trinomial f'(x,y) = x^2 - 7xy - 30y^2 = (x + p')(x + q')
Find two quantities knowing sum (-7y) and product (-30y^2).
They are: p' = 3y and q' = - 10y --> sum (-7y) and product (-30y^2)
Back to trinomial f(x,y), $p = \frac{p '}{a} = \frac{3 y}{5}$ and
$q = \frac{q '}{a} = \frac{- 10 y}{5} = - 2 y$.

Factored form:$f \left(x , y\right) = 5 \left(x + \frac{3 y}{5}\right) \left(x - 2 y\right) = \left(5 x + 3 y\right) \left(x - 2 y\right)$