I need to prove that $x^5+5x^2+4$ is irreducible over $\mathbb{Q}(\zeta_5)$. I can see that is irreducible over $\mathbb{Q}$ using reduction $\pmod5$, but how can I conclude?
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What is $\zeta_5$ – Learnmore Jan 02 '16 at 03:46
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a primitive fifth root of unity – Morton Jan 02 '16 at 03:46
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3Is the assertion being made that $x^5+5x^2+4$ is irreducible mod $5$? If so I do not understand it, since there is a root modulo $5$. – André Nicolas Jan 02 '16 at 03:56