How do you factor #9x^2 + 6x - 8#?

1 Answer
Nghi N.
May 27, 2015

f(x) = 9x^2 + 6x - 8 = (x - p)(x - q)
Use the new AC Method
Convert f(x) to f'(x) = x^2 + 6c - 72. Compose factor pairs of (-72).
Proceed: ...(-4, 18)(-6, 12). This sum is 6 = b. Then p' = -6 and q' = 12.
Then #p = (p')/a = -6/9 = -2/3, #and #q = (q')/a = 12/9 = 4/3#.

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

Check by developing:# f(x) = 9x^2 + 12x - 6x - 8.# OK

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