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

F(x) has roots -9, and 7 - i.

Therefore  x = -9,                            x = 7 -i

x + 9 = 0                                          x - 7 + i = 0 

(x + 9) must be a factor.                (x + i - 7) must also be a factor.

Therefore (x + 9) and (x + i - 7) must be factors.