Mathematics

Problem

A monic cubic polynomial has

-2

0

, and

\tfrac{1}{2}

as its zeros. a. (i) Construct this monic cubic polynomial in standard form. b. (ii) Multiply the polynomial obtained in part (i) by

4

so that the coefficient of

x^{3}

becomes

4

. Write the new polynomial explicitly. c. (iii) Evaluate the polynomial of part (ii) at

x=-1

and hence state the remainder when it is divided by

(x+1)