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. Ay intercept of f(x) is x = 2k.​

Answer 1

A. f(2k) = 0

Explanation:

Answer 2

A. f(2k)=0

Explanation:

The factor theorem states that a polynomial f(x) has a factor (x−k) if and only if f(k)=0 (i.e. k is a root).

If (x – 2k) is a factor of f(x), then by the factor theorem f(2k)=0 (i.e. 2k is a root).

Option A is true, f(2k)=0

Option B is false, it should be like in option A, f(2k)=0

Option C is false, because x=2k is a root, not x=-2k

Option D is false, because x-intercept of f(x) is x=2k, not y-intercept.