Answer the questions that follow concerning zeros of a cubic polynomial.
a. (a) State the Factor Theorem.
b. (b) Explain why, if a and b are two distinct zeros of a cubic polynomial h(x), then (x−a)(x−b) must divide h(x).
c. (c) A cubic polynomial h(x) has zeros 2 and −3. Give a reasoned argument to show that h(x) can be written as (x−2)(x+3)(x−k) for some real number k.
d. (d) If h(x)=x3+px2+qx+r, express p in terms of the three zeros and describe, in words, how the value of k could be found once p is known.