Irreduciblity of polynomial in $\Bbb Q[x]$

Question

I am trying to prove that $x^5 + 16$ is irreducible in $\Bbb Q[x]$. (Hint: Consider $(x-1)^5 + 16$)

Not sure how to use the hint, thanks for any help in advance.

Expand $(x-1)^5+16$ and use Eisenstein's criterion. – Sungjin Kim May 14 '13 at 20:36 — Sungjin Kim, May 14 '13 at 20:36

Git Gud · Answer 1 · 2013-05-14T20:46:24.673

2

Second hint: $x^5+16$ is irreducible over $\Bbb Q$ if, (and only if), $(x-1)^5+16$ is irreducible over $\Bbb Q$.

edited May 14 '13 at 20:46

answered May 14 '13 at 20:37

Git Gud

1 Answers1