How do you factor 12w^2+w-612w2+w−6?

1 Answer
Nghi N.
May 10, 2016

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

Explanation:

y = 12w^2 + w - 6.y=12w2+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)

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