Let , , and (the zero being repeated) be the zeros of a cubic polynomial…
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Let 2, −1, and −1 (the zero −1 being repeated) be the zeros of a cubic polynomial p(x).
(i) Construct the monic cubic polynomial having the given zeros.
(ii) A new polynomial q(x) is formed by multiplying the polynomial in part (i) by 2. Write q(x) explicitly and state its leading coefficient.
(iii) Calculate q(1) and interpret its value in the context of the remainder theorem.