For the Complex Polynomial Below, One of Its Zeroes Is

question 68

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

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