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Mathematics

A polynomial function f has x+8 as a factor. Which of the following must be true about the function f?

I.f(0)=8
II.f(8)=0
III.f(-8)=0

A.I only
B.II only
C.III only
D.II and III only

答案和解析

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.