How do you factor #15x^2-2x-8#?

1 Answer
Nghi N.
Oct 17, 2015

Factor #y = 15x^2 - 2x - 8#

Ans: #y = (3x + 2)(5x - 4).#

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
#y = 15x^2 - 2x - 8 =# 15(x + p) (x + q)
Converted #y' = x^2 - 2x - 120 =# (x + p')(x + q').
p' and q' have opposite signs. Factor pairs of ac = -120 --> ...(-4, 30)(-5, 24)(-10, 12), This sum is 2 = -b. Then, the opposite sum gives p' = 10 and q' = -12.
Therefor, #p = (p')/a = 10/15 = 2/3# and #q = (q')/a = -12/15 = -4/5#.
Factored form: #y = 15(x + 2/3)(x - 4/5) = (3x + 2)(5x - 4).#

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