How do you show that $x^n+x+3$ is irreducible for all $n \ge 2$?
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I think rational root theorem and primality of $3$ might help. – Prasun Biswas Mar 25 '15 at 19:01
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Rational root theorem helps to show polynomials do not have a linear divisor, but not that they have no polynomial divisors. @PrasunBiswas – Thomas Andrews Mar 25 '15 at 19:02
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Ah, then I have no idea for the proof. :P @ThomasAndrews – Prasun Biswas Mar 25 '15 at 19:08
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Irreducible over the integers, or irreducible over the real numbers? – Tim Raczkowski Mar 25 '15 at 19:12
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1@user142671 Are you in the same class(room of test) with SamJ ? – Olórin Mar 25 '15 at 19:15