Question

How do you factor `3p^2 + 2p - 16 = 0`?

Answer 1

Factor f(x) = 3x^2 + 2x - 16 = (x - p)(x - q).
I use the new AC Method.
Converted f(x) --> `f'(x) = x^2 + 2x _ 48`= (x - p')(x - q').

Find p' and q' by composing factor pairs of a.c = -48 -> (-4, 12)(-6, 8). This sum is 2 = b. Then p' = -6 and q' = 8.

Then`p = (p')/a = -6/3 = -2` and `q = (q')/a = 8/3`

Factored form: `f(x) = (x - 2)(x + 8/3) = (x - 2)(3x + 8).`

Check by developing: `f(x) = 3x^2 + 8x - 6x - 16`. OK