I'm having trouble thinking this out.

I have this problem:

Suppose that for all x in (−c, c) the identity

a0 + a1x + .... + an-1x^(n-1) + (an + A(x))x^n = b0 + b1x + .... + bn-1x^(n-1) + (bn + B(x))x^n, where the limit as x goes to 0 of A(x) = lim as x goes to 0 of B(x) = 0. How would I show that a0 = b0, a1 = b1, ...... , an = bn. It seems to make sense, but I'm not quite show sure how to show it. How would you do it? Thanks for any help on this.