## Zero Polynomial problem

Let $A \in R[x]$ have degree $n \geq 0$ and let $B \in R[x]$ with degree of at least 1 with the leading coefficient of B being a unit of R. Then by a problem I posted earlier, we know that there exist unique polynomials $Q_0,Q_1,...Q_n \in R[x]$ such that $deg Q_i < deg B \ \ \ \forall i$. Prove that if $deg(B)=1$, then $Q_n$ is not the zero polynomial.

Idea so far.

So if the degree of B is 1, then the degree of $Q_n$ is less than 1, so does that force it to be a constant polynomial that is not 0 since the leading coefficient is a unit?

Thank you.