Answer the following questions related to zeros of polynomials:
MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Answer the following questions related to zeros of polynomials:
(i) State the Factor Theorem for polynomials.
(ii) Explain, with reason, why if a cubic polynomial p(x) satisfies p(3)=0, then (x−3) must divide p(x) exactly.
(iii) For the polynomial p(x)=x3−6x2+11x−6, verify the statement made in part (ii) and then factorise p(x) completely into linear factors.