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im teeching algebra and had to prove that X^5 - 8 was irreducible over the rationals. so i did it using eisenstein.
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 I am teching does not have that in it.
is there an easier proof? I am a rookie at this stuff.
thanks
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 I am teching does not have that in it.
is there an easier proof? I am a rookie at this stuff.
thanks