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SamuelRSmith said:
Factor theorem? Input values -4 to 4 (excluding zero) into the function. If the answer comnes up with a zero, then you have one of the possible answers.

Then divide the function by the factor, getting the rest of the factors should be easy from then on in.

Chances are one of the factors are between -4 and 4, so this sounds like a good place to start.

Unfortunately exluding zero from your calculation is basically giving him the answer.  Since the differentiation of a |f(x)| function has no value when x=0 you have given him the answer to the second part of the question :)