How do you factor #6x^2+5x-4#?

1 Answer
Nghi N.
May 28, 2016

(2x - 1)( 3x + 4)

Explanation:

Use the new AC Method (Socratic Search)
#y = 6x^2 + 5x - 4 =# 6(x + p)(x + q)
Converted trinomial: #y' = x^2 + 5x - 24 =# (x + p')(x + q').
p' and q' have opposite signs because ac < 0.
factor pairs of (ac = - 24) --> (-3, 8). This sum is (5 = b). Then p' = -3 and q' = 8.
Back to trinomial y --> #p = (p')/a = -3/6 = -1/2#, and #q = (q')/a = 8/6 = 4/3#.
Factored form #y = 6(x - 1/2)(x + 4/3) = (2x - 1)(3x + 4)#

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