Your Answer is

Correct Answer is B

Explanation

According to the meaning of the question, (x+k) is a factor of x²-kx-8=0, so we can know x²-kx-8 by large division =(x+k)(x-2k), that is, x²-kx-8=x²-kx-2k², so -8=-2k²，k=-2, 2, so choose B