Assignment:
Find the polynomials that represent 1/x^3+x , x/x^3+x, x^2/x^3+x, and x^3/x^3+x modulo the irrreducible polynomial x^5+x^2+1 over F2 ( the field with two elements 0 and 1)
Your answers should be polynomials over F2 with degrees at most four. (Can you explain in here why at most degree four)
Note: Use the Eucliden algorithm for polynomials. (Can you do this algorithm step by step to understand).
Provide complete and step by step solution for the question and show calculations and use formulas.