Quiz (Complex and Rational Zeros of Polynomials)

Show all work and justify each step.

(1) Find the remainder when



is divided by without using synthetic division or long division.

(2) List the roots of the polynomial



and state the multiplicity of each.

(3) Write as a product of linear factors.

(4) Determine a polynomial of lowest degree with roots 2 (of multiplicity 3), and with real coefficients.

(5) Determine a polynomial of lowest degree with roots (of multiplicity 2) and with real coefficients.

(6)  Determine a polynomial of lowest degree with roots and with integer coefficients.

(7) Solve the equation