Assume $A, B \in \mathbb{Z}^+$. If $x^A(1 - x)^B$ is divided by $(1 + x^2)$, the remainder is $ax + b$, show that $a = (\sqrt{2})^B \sin\frac{(2A - B)\pi}{4}$ and $b = (\sqrt{2})^B \cos\frac{(2A - B)\pi}{4}$
So, I guess I have something like:
$g(x)(1+x^2) = ax + b$
Without a value to sub in, I am not sure how I proceed. Where should I go with this? I'm not sure how the sin and cos will appear.