If a polynomial function f(x) has roots 4-13i and 5, what must be a factor of f(x)? a. (x+(13-4i)) b. (x-(13+4i)) c. (x+(4+13i)) d. (x-(4+13i))

a polynomial has real valued coefients

if a function with real coeffients has a root (a+bi), then (a-bi) must also be a root (multiplying them gives real values)

if f(x) has roots a, b, c, then it can be factored into

f(x)=(x-a)(x-b)(x-c)

since 4-13i is a root, then 4+13i must also be a root

roots are 4-13i, 4+13i, and 5

so the function must be able to have factors (x-(4-13i)), (x-(4+13i)), and (x-5)

you can see that D is (x-(4+13))

so the answer is D

the answer is d

Step-by-step explanation: