Question

How do you fzctor `-13w - 20+ 15w ^ { 2}`?

Answer 1

(5x + 4)(3x - 5)

Explanation:

`y = 15w^2 - 13w - 20 =` a(w + p)(w + q)
Use the new AC Method to factor trinomials (Socratic, Google Search)
Converted trinomial:
`y' = w^2 - 13w - 300 =` (w + p')(w + q')
Proceeding: Find 2 numbers p' and q', knowing sum (b = -13) and product (ac = - 300). Then, divide them by a = 15.
The factor pair (12, -25) fits. Then, p' = 12 and q' = - 25.
Back to y, -->`p = (p')/a = 12/15 = 4/5`, and `q = (q')/a = - 25/15` = -5/3.
Factored form:
y = 15(w -+4/5)(w - 5/3) = (5w + 4)(3w - 5).