For a polynomial function p, a real number r is a root of p if and only if p(x) is evenly divisible by x_r. This fact leads to one of the important properties of polynomial functions: a polynomial of degree d can have at most d roots. This is the first of a sequence of problems aiming at showing this fact.

This task continues ``Zeroes and factorization of a quadratic polynomial I.'' The argument here generalizes, as shown in ``Zeroes and factorization of a general polynomial'' to show that a polynomial of degree d can have at most d roots. This task is intended for instructional purposes to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions.