Question

If (x – 2k) is a factor of f(x), which of the following must be true?
f(2k) = 0
f(–2k) = 0
A root of f(x) is x = –2k.
A y intercept of f(x) is x = 2k.

Answer 1

Only "f(2k) = 0" must be true.

Reason: By the factor theorem, if (x − 2k) is a factor then f(2k) = 0, so x = 2k is a root. f(−2k) need not be 0 (unless k = 0), "x = −2k" is not the root, and the y‑intercept occurs at x = 0, not x = 2k.