For the Complex Polynomial Below, One of Its Zeroes Is

Short Answer

For the complex polynomial below, one of its zeroes is z = 5i. 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(z) = z³ + (1 - 5i)z² + (-6 - 5i)z + 30i.