im teeching algebra and had to prove that X^5 - 8 was irreducible over the rationals. so i did it using eisenstein.(adsbygoogle = window.adsbygoogle || []).push({});

then more generally i seem to have proved that X^n - a is irreducible over the rationals whenever it has no rational root.

but i used galois theory, and the course im teching does not have that in it.

is there an easier proof? im a rookie at this stuff.

thanks

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# Irreducible polynomials

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