Is the polynomial $x^n+2x^{n-1}+\dots+nx+n+1$ irreducible in $\mathbb Z[x]$?
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3Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Aug 21 '19 at 15:55
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Hint: This is $\frac{f(x)}{(x-1)^2}$ for a nicer polynomial $f$ – Hagen von Eitzen Aug 21 '19 at 16:02
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The case when $n+1$ is a prime number was handled here in a nice way. – Jyrki Lahtonen Aug 21 '19 at 18:00
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2Possible duplicate of Family of irreducible polynomials. No answer there that would cover all $n$ either. Feels a bit taxing. – Jyrki Lahtonen Aug 21 '19 at 18:05