Let $P(x) =1+x+x^2+x^3+x^4+x^5$. What is the remainder when $P(x^{12})$ is divided by $P(x)$?
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should there be exponents? – Asinomás Sep 22 '16 at 16:36
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When you work with higher degree polynomial and carry out multiplication and division you are not doing Linear Algebra. – P Vanchinathan Sep 22 '16 at 16:39
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Related. – Jyrki Lahtonen Sep 22 '16 at 17:09
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Please improve your question by mentioning your attempts. There is an interesting interpolation approach related with the sixth roots of unity. – Jack D'Aurizio Sep 23 '16 at 00:45
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In particular, the remainder is $\color{red}{6}$ because the value of $Q(x)=P(x^{12})$ at any sixth root of unity is six. – Jack D'Aurizio Sep 23 '16 at 00:53
