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.