If (x - 2k) is a factor of f (x), which of the following must be true?

a) f (2k) = 0

b) f (-2k) = 0

c) A root of f (x) is x = - 2k.

d) A y intercept of f (x) is x = 2k.

(x-2k) is a root of a polynomial by the Zero Product Property that states (for this particular function) (x-2k) = 0 and x=2k. That means that this is an x-intercept of the function and f (2k) which is your y is zero at the x-intercept. So your answer is a, f (2k) = 0