MATHEMATICS · Subjective · GCSE · Further Mathematics · Algebra and Proof · Algebra and Proof
Problem
Prove the following statements:
(i) For any polynomial p(x), the product p(x)×0 is the zero polynomial.
(ii) Hence, discuss why assigning a numerical degree to the zero polynomial leads to a contradiction with the rule deg(p(x)q(x))=degp(x)+degq(x) that holds for non-zero polynomials.
(iii) If a polynomial p(x) is divided by another non-zero polynomial g(x) and the remainder obtained is the zero polynomial, show that g(x) is a factor of p(x).