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答案：C
解析：
Choice C is correct. Recall that if x-k is a factor of a polynomial P, then P(k)=0.
It is given that x+8 or x-(-8) is a factor of f.
Therefore, it follows that f(-8)=0.
It is not known whether or not x-8 is a factor of f and so we cannot say whether or not f(8)=0.
Additionally, no other information about function f is given, and so we do not know whether or not f(0)=8.
Therefore, I and II may or may not be true, but III must be true.
