The remainder of $$f(x)=x^{100}+x^{50}+x^{10}+x^2-6$$ when divided by $$x^2-1$$ is

Solution

Modulo $$x^2-1$$, we have $$x^2=1$$. Therefore every even power of $$x$$ is congruent to $$1$$, so the polynomial is congruent to $$1+1+1+1-6=-2$$. Hence the remainder is $$-2$$.

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