Question

How do you factor `12x^2 + 100x - 72`?

Answer 1

4(3x - 2)(x + 9)

Explanation:

`f(x) = 4y = 4(3x^2 + 25x - 18)`
Factor y by the new AC Method (Socratic Search).
`y = (3x^2 + 25x - 18) =` 3(x + p)(x + q)
Converted trinomial: `y' = x^2 + 25x - 54 =` (x + p')(x + q')
p' and q' have opposite signs because ac < 0.
Factor pairs of (ac = -54) -->...(-2, 27). This sum is 25 = b. Then, p' = -2 and q' = 27.
Back to original trinomial y --> `p = (p')/a = -2/3`, and
`q = (q')/a = 27/3 = 9`.
Factored form: `y = 3(x - 2/3)(x + 9) = (3x - 2)(x + 9).`
Therefor,

f(x) = 4y = 4(3x - 2)(x + 9)