Answer:
f(x) = x³ + 5x² + 4x + 40
Explanation:
We know
Zeros: -5, -2i
Write a polynomial function in standard form.
-2i is a complex number, its conjugate is 2i, which is also a zero of the polynomial.
We write:
f(x) = (x - (-5))(x - (-2i))(x - 2i)
f(x) = (x + 5) (x + 2i) (x - 2i)
f(x) = (x + 5) (x² - 4i²)
i² = -1
f(x) = (x + 5) (x² - 4(-1))
f(x) = (x + 5) (x² + 4)
f(x) = x³ + 4x + 5x² + 40
f(x) = x³ + 5x² + 4x + 40
So, the answer is f(x) = x³ + 5x² + 4x + 40