In: Advanced Math
Proposition 6.18 (Division Algorithm for Polynomials). Let n(x) be a polynomial that is not zero. For every polynomial m(x), there exist polynomials q(x) and r(x) such that
m(x) = q(x)n(x) +r(x)
and either r(x) is zero or the degree of r(x) is smaller than the degree of n(x).
Prove