(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

M and N are positive integers with M>N. The division algorithm for integers tells us there exists integers Q and R such that M=QN+R with 0[tex]\leq[/tex]R<N. The division algorithm for real polynomials tells us that there exist real polynomials q and r such that x^{M}- 1 = q(x^{N}- 1) + r with r = 0 or deg r < N. Find q and r.

2. Relevant equations

3. The attempt at a solution

I have rewritten it as x^{QN+R}- 1 = q(x^{N}- 1) + r, so I think q must be of degree QN+R-N = N(Q-1)+R

However, it is not then always (in fact more likely not) true that N(Q-1)+R<N so 1 must have more than 1 term. But I am struggling to know where to go from here.

Thanks for any help :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Division algorithm for polynomials

**Physics Forums | Science Articles, Homework Help, Discussion**