Question

If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)?

Answer 1

see explanation

Explanation:

If a polynomial has roots x = a, x = b, x = c then

(x - a), (x - b) and (x - c) are the factors of the polynomial.

Note that complex roots occur in conjugate pairs, thus

x = - i is a root then so is x = i

given f(x) has roots

x = - 9, x = 7 and x = - i, x = i, then

(x + 9), (x - 7), (x + i), (x - i) are the factors of f(x)

Answer 2

A. (x - (7 + i))