Let $\displaystyle A \in R[x] $ have degree $\displaystyle n \geq 0 $ and let $\displaystyle B \in R[x] $ have degree at least 1. Prove that if the leading coefficient of B is a unit of R, then there exist unique polynomials $\displaystyle Q_0,Q_1,...,Q_n \in R[x] $ such that $\displaystyle deg Q_i < deg B $ for all i and $\displaystyle A = Q_0+Q_1B+...+Q_nB^n$.

I'm a bit threw off by this problem, if B is a unit of R, what would that do?