How do you factor #-27x^2 + 18x + 24#?

1 Answer
Nghi N.
Oct 9, 2015

Factor #f(x) = -27x^2 + 18x + 24#

Ans: #f(x) = -3(3x - 2)(3x + 4)#

Explanation:

First, put -3 in common factor -->
#f(x) = -3y = (-3)(9x^2 - 6x - 8)#
Next, factor #y = 9x^2 - 6x - 8 =# 9(x + p)(x + q)
I use the new AC Method (Socratic Search).
Converted #y' = x^2 - 6x - 72 = #(x + p')(x + q').
p' and q' have opposite signs. Factor pairs of (-72) --> (-2, 36)(-3, 24)(-6, 12). This sum is 6 = -b. The opposite sum gives p' = -6 and q' = 12. Therefor, #p = (p')/a = -6/9 = -2/3# and #q = 12/9 = 4/3#.
Factored form of #y = 9(x - 2/3)( x + 4/3) = (3x - 2)(3x + 4)#

Factored form of #f(x) = -3(3x - 2)(3x + 4)#

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