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Luv2Teach
By the conjugate root theorem if we have 7-i as a root we have to have 7+i as a root also.  Written in factor form, they are (x-(7-i)) and (x-(7+i)).  You could rewrite and remove the inner set of parenthesis, but the second of those is what you need.  It's choice one above.

Answer:

[tex](x-(7+i))[/tex] is the answer

Step-by-step explanation:

a polynomial function f(x) has roots -9 and 7-i

Polynomial roots always come with conjugate pairs

7-i is one of the root

7+i is the another root

So we have three roots

If 'a' is a root then (x-a) is a factor

-9 is one of the root , factor is (x+9)

7-i is a root then factor is [tex](x-(7-i))[/tex]

7+i is a root then factor is [tex](x-(7+i))[/tex]

[tex](x-(7+i))[/tex] is the answer

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