For the Complex Polynomial Below, One of Its Zeroes Is

Multiple Choice

For the complex polynomial below, one of its zeroes is x = 3 - i. Use the given zero to help find all zeroes of the polynomial, then write the polynomial in completely factored form. Hint: synthetic division and the quadratic formula can be applied to all polynomials, even those with complex coefficients. C(x) = x³ - 3x² + (3 + 3i) x + (-6 + 2i)

A) C(x) = (x - 3 - i) (x + 2i) (x + i) ; x = -2i, x = -i
B) C(x) = (x - 3 + i) (x - 2i) (x - i) ; x = 2i, x = i
C) C(x) = (x - 3 + i) (x + 2i) (x - i) ; x = -2i, x = i
D) C(x) = (x - 3 + i) (x - 2i) (x + i) ; x = 2i, x = -i