Question

How do you factor `3x^2 + 2x - 8`?

Answer 1

f(x) = 3x^2 + 2x - 8 = (x - p)(x - q).
Convert f(x) to f'(x) = x^2 + 2x - 24 = (x - p')(x - q'). Compose factor pairs of (a.c = - 24) --> (-2, 12)(-3, 8)(-4, 6). This last sum is 2 = b. Then,
p' = -4 and q' = 6.
Then, p = (p')/a = -4/3, and q = (q')/a = 6/3 = 2.
Factored form: f(x) = (x - 4/3)(x + 2) = (3x - 4)(x + 2)

Check by developing:
f(x) = 3x^2 + 6x - 4x - 8. OK