If open paren x minus 2 k close paren is a factor of f of x , which of the following must be true?

By the Factor Theorem, if (x − 2k) is a factor of f(x), then substituting x = 2k makes that factor zero, so f(2k) = 0. Therefore, 2k is a root of f(x), which is exactly the statement in choice A. The negative sign in choices C and D does not follow from the given factor.

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