Given that 3x^3 + 4x^2 - 13x - 12 = (Ax + 1)(x + B)(x -3) + C for all values of x, find the values of A, B and C.

What I did:

f(x) = 3x^3 + 4x^2 - 13x - 12

A = 3 (by inspection)

C = f(3) = 66

My questions:

1. Why is it not possible to find C by subsituting -(1/3) into x, since (3x + 1) would = 0?

2. How do I solve for B? (Ans: 4)