Question

How do you factor `15x^2-2x-8`?

Answer 1

Factor `y = 15x^2 - 2x - 8`

Ans: `y = (3x + 2)(5x - 4).`

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
`y = 15x^2 - 2x - 8 =` 15(x + p) (x + q)
Converted `y' = x^2 - 2x - 120 =` (x + p')(x + q').
p' and q' have opposite signs. Factor pairs of ac = -120 --> ...(-4, 30)(-5, 24)(-10, 12), This sum is 2 = -b. Then, the opposite sum gives p' = 10 and q' = -12.
Therefor, `p = (p')/a = 10/15 = 2/3` and `q = (q')/a = -12/15 = -4/5`.
Factored form: `y = 15(x + 2/3)(x - 4/5) = (3x + 2)(5x - 4).`