Question

How do you factor `3y^2 - 14y - 5`?

Answer 1

(3y + 1)(y - 5)

Explanation:

Use the new AC Method (Socratic Search)
`f(y) = 3y^2 - 14y - 5 =` 3(x + p)(x + q)
Converted trinomial `f'(y) = y^2 - 14y - 15 =` (x + p')(x + q')
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = -15) --> (-1, 15)(1, -15). This sum is (-14 = b). Then p' = 1 and q' = -15.
Back to original trinomial f(y), `p = (p')/a = 1/3`and `q = (q')/a = -15/3 = -5`.
Factored form `f(y) = 3(y + 1/3)(y - 5) = (3y + 1)(y - 5)`