A teacher gave her students the following question as a practice problem to informally assess their understanding of factoring and complex numbers.
Problem: Completely factor the polynomial z³-5x²+3x-15
Student solution: (x²+3) (2-5)
Which of the following statements should the teacher have included to prompt students into giving the answer as
(z+i√3) (zi√3) (25), where i = √I?
a. Completely factor the polynomial into the product of factors with real coefficients.
b. Completely factor the polynomial into the product of factors with rational coefficients.
c. Completely factor the polynomial into the product of factors with complex coefficients.