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Is it divisible?

Algebra Level 3

\(x^{9999}+x^{8888}+x^{7777}+ \cdots+x^{1111}+x^{0}\) is divisible by which of the following polynomials?

\[x-1\] \[x+1\] \[x^{8}+x^{6}+x^{4}+x^{2}\] \[x^{9}+x^{7}+x^{5}+x^{3}+x\]

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by Piyush Kumar Behera

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