Question

Find a degree 3 polynomial with real coefficients having zeros 2 and 4 − 4 i and a lead coefficient of 1. Write P in expanded form.

Answer 1

p(x) = x^3 - 10x^2 + 48x - 64

Explanation:

p(x) = (x-2)(x-(4-4i))(x-(4+4i))

p(x) = )x-2)((x-4)+4i)((x-4)-4i)

p(x) = (x-2)((x-4)^2 - (4i)^2)

p(x) = (x-2)(x^2-8x+16+16)