Question

How do you factor `20+13w-15w^2`?

Answer 1

The best method to me is the new AC Method to factor trinomials. It is similar to the existing factoring AC Method. This method is fast, systematic, no guessing, no factoring by grouping and no solving binomials.
y = - (15x^2 - 13x - 20) = - (x - p)(x -q)
Converted trinomial: x^2 - 13x - 300 = (x - p')(x - q').
Find p' and q' by composing factor pairs of a.c = -300 --> (-10, 30)(-12, 25). This last sum is 13 = -b. Then, p' = 12 and q' = -25. Back to original trinomial y --> p = p'/a = 12/15 = 4/5, and q = q'/a = -25/15 = -5/3

Factored form: y = -(x + 4/5)(x - 5/3) = -(5x + 4)(3x - 5) =
= - (15x^2 - 13x - 20) = -15x^2 + 13x + 20. OK