Letf eR[x] where R is a commutative ring. If f has form
a(subn)x^n + ... + a1x + a0 with an a(subn) != 0 then the degree of f is defined to be n and the leading coefficient is defined to be an.
Iff, g eF[x] are non-zero polynomials where F is a field,
deg(fg) = deg f + deg g
Justify the above theorem. Explain why the proof does
not work if the coefficients are in Zm where m is composite. Hint: focus on the leading coefficients.