Question

How do you factor `15y^2 + 26y +8=0`?

Answer 1

(5y + 2)(3y + 4)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
`f(y) = 15y^2 + 26y + 8 =`15(y + p)(y + q).
Converted trinomial `f'(y) = y^2 + 26y + 120 =` (y + p')(y + q').
p' and q' have same sign because ac > 0.
Factor pairs of (ac = 120) --> ...(`5, 24)(6, 20).` This sum is (26 = b). Therefor, p' = 6 and q' = 20.
Back to original trinomial y --> `p = (p')/a = 6/15 = 2/5` and
`q = (q')/a = 20/15 = 4/3`
Factored for --> f(y) = 15(y + 2/5)(y + 4/3) = (5y + 2)(3y + 4)