Question

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))

Answer 1

when your roots are "a" and "-b" the factors of the function are,
(x-a) and (x+b)
and function is as follows,
f(x) = (x-a)(x+b)

Answer 2

"x minus the additive inverse of the root" this is inside the parenthesis.

Answer 3

do you want to see an example similar to yours ?

Answer 4

no thanks I got it thank you

Answer 5

I think that your answers are not correct.
It is supposed to be a product (multiplication) of factors, so that a root would make one part of the product a zero, so that you get a zero for f(x) (when you plug in the value of the root instead of x)

Your choices however are either wrong, or have some typo....

Answer 6

For roots "d" and "f" it is supposed to be
\(\large\color{black}{f(x)=(x-d)(x-f) }\)
in other words,
\(\large\color{black}{f(x)=(x-d) \color{blue}{\LARGE\times}(x-f) }\)

Not,
\(\large\color{black}{f(x)=(x-d) \color{red}{-}(x-f) }\)
and NOT
\(\large\color{black}{f(x)=(x-d) \color{red}{+}(x-f) }\)

and not even
\(\large\color{black}{f(x)=(x-d) \color{red}{\div}(x-f) }\)
(in this scenario, the "f" is when function is undefined, not a root.