How do you factor the trinomial #2x^2 + 9x - 5 = 0#?

1 Answer
Nghi N.
Jan 10, 2016

(2x - 1)(x + 5)

Explanation:

I use the new AC Method to factor trinomials (Socratic Search)
#y = 2x^2 + 9x - 5 =# 2(x + p)(x + q) (1)
Converted trinomial #y' = x^2 + 9x - 10 =# (x + p')(x + q').
p' and q' have opposite signs because ac < 0
Factor pairs of ac = -10 --> (-1, 10). This sum = 9 = b.
Then, p' = -1 and q' = 10.
Back to trinomial (1): #p = (p')/a = -1/2# and #q = (q')/a = 10/2 = 5#

Factored form: #y = 2(x - 1/2)(x + 5) = (2x - 1)(x + 5)#

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