write f(x) as a product of linear factors

Question

Given the fact that 2+i and -i are zeros of f(x), write f(x) as a product of linear factors.

Answer 1

Four of the factors are

(x - (2 + i))(x - (2 + i))(x + i)(x - i)

These reduce to

(x² - 4x + 5)(x² + 1)

Now use long division to suppress the given function.