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

Rule: if k is a root of f(x) then x-k is a factor of f(x)

So if k = -9, is a root then x-k = x-(-9) = x+9 is a factor. The expression x+9 isn't listed so we'll move on



Another root is k = 7-i so another factor would be x-k = x-(7-i) = x-7+i
this isn't listed either so we move on



If 7-i is a root, then so is 7+i which is the complex conjugate of 7-i

If k = 7+i is a root, then x-k = x-(7+i) is a factor. This is listed as choice A



Final Choice A