When x+x1998+x1999+x2000+x2001 is divided by x3-x, find the remainder
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Let your polynomial be p(x). Then p(x)=(x3-x)q(x) + ax2 + bx + c where a, b and c are unknowns to be determined. Evaluate this equation at x=0, 1 and -1. You should then be able to find the unknowns.
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