Question

How do you factor `12w^2+w-6`?

Answer 1

(3w - 2)(4w + 3)

Explanation:

`y = 12w^2 + w - 6.` = 15 (w + p)(w + q)
Use the new AC Method (Socratic Search)
Converted trinomial: `y' = w^2 + w - 72 =` (w + p')(w + q').
p' and q' have opposite sign because ac < 0.
Factor pairs of (ac = -72) -->...(-6, 12) (-8, 9). This sum is (1 = b). Then, p' = -8 and q' = 9.
Back to original y, `p = (p')/a = -8/12 = -2/3`, and `q = (q')/a = 9/12 = 3/4.`
Factored form `y = 15(w - 2/3)(w + 3/4) = (3w - 2)(4w + 3)`