Question

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

Answer 1

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)`