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

The answer is (A) (x - (7 + i)).

Step-by-step explanation:  Given that a polynomial function f(x) has roots -9 and (7 - i).

Since (7 - i) is a root of the polynomial f(x), so its conjugate will also be a root of f(x) because the complex roots always occur in pairs.

Therefore, (7 + i), which is the conjugate of (7 - i) will also be a root of f(x).

So, the factor (x - (7 + i)) will be a factor of the given polynomial f(x).

Thus, (A) is the correct option.

A.(x – (7 + i))

Step-by-step explanation:

When we have roots of a polynomial that a complex, the come in complex conjugate pairs.  That is if one roots is a+bit, another root must be a-bi

Since one root is 7-i, there is another root that is 7+i

We write the factors as (x- root)

(x- (7+i))

(x - (7+i))