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

For a polynomial with real coefficients, any nonreal root must come with its complex conjugate. Since 7 − i is a root, 7 + i must also be a root. A root r gives the factor x − r, so the required factor is x − (7 + i), choice A.

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