How do you factor #5x^(2) - 7xy - 6y^(2)#?
(5x + 3y)(x - 2y)
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),