Question

How do you factor `12x^2+28x-5`?

Answer 1

(6x - 1)(2x + 5)

Explanation:

Use the new AC Method (Socratic Search)
`y = 12x^2 + 28x - 5 =` 12(x + p)(x + q)
Converted trinomial: `y' = x^2 + 28x - 60 =` (x + p')(x + q').
p' and q' have opposite sign because ac < 0.
Factor pairs of ac = -60) --> (-2, 30). This sum is 28 = b. Then, p' = -2 and q' = 30.
Back to original trinomialy, `p = (p')/a = -2/12 = -1/6`, and
`q = (q')/a = 30/12 = 5/2`
Factored from: `y = 12(x - 1/6)(x + 5/2) = (6x - 1)(2x + 5)`