Question

How do you factor the expression #12w^2 - 13w - 35?

Answer 1

y = (4x + 5)(3x - 7)

Explanation:

Use the new systematic AC Method to factor trinomials (Socratic Search)
`y = 12x^2 - 13x - 35 =` 12(x + p)(x + q).
Converted trinomial: `y' = x^2 - 13x - 420 =` (x + p')(x + q').
p' and q' have opposite signs.
Compose factor pairs of (ac = -420) -->...(-12, 35)(-15, 28). This sum is
(28 - 15 = 13 = -b). Then, the opposite sum (15, -28) gives: p' = 15 and q' = -28.
Back to original trinomial: `p = (p')/a = 15/12 = 5/4` and `q = (q')/a = -28/12 = -7/3.`
Factored form:
`y = 12(x + 5/4)(x - 7/3) = (4x + 5)(3x - 7)`