Find a degree 3 polynomial with real coefficients having zeros 3 and 3-3i and a lead coefficient of 1. Write P in expanded form.

P = x³ - 9x² + 36x - 54

Step-by-step explanation:

Complex roots come in conjugate pairs. So if 3-3i is a zero, then 3+3i is also a zero.

P = (x - 3) (x - (3-3i)) (x - (3+3i))

P = (x - 3) (x - 3 + 3i) (x - 3 - 3i)

P = (x - 3) ((x - 3) ² - (3i) ²)

P = (x - 3) ((x - 3) ² + 9)

P = (x - 3) ³ + 9 (x - 3)

P = x³ - 9x² + 27x - 27 + 9x - 27

P = x³ - 9x² + 36x - 54