Answer:
see explanation
Step-by-step explanation:
(1)
Complex roots occur in conjugate pairs.
Given x = - 3i is a zero, then x = + 3i is also a zero
(2)
Given the zeros x = - 4, x = 3i, x = - 3i, then the factors are
(x + 4), (x - 3i) and (x - (- 3i)), that is
(x + 4), (x - 3i), (x + 3i) and the polynomial is the product of the factors
f(x) = (x + 4)(x - 3i)(x + 3i) ← expand complex factors
= (x + 4)(x² - 9i²) → i² = - 1, so
= (x + 4)(x² + 9) ← distribute factors
= x³ + 9x + 4x² + 36
= x³ + 4x² + 9x + 36
