Irreducible Polynomial (or not?)

[danieldf]

The polynomial is x^n + A1x^(n-1) + A2x^(n-2) + ... + A2x^2 + A1x + 1. Where An (integer) is not zero for all n and n is even. For example: x²+x+1; x^4+2x^3+3x^2+2x+1.
I'm looking for a method to say if that kind of polynomial is irreducible over racionals... Or when it is.

Thx!

 

[Petek]

Are A1, A2,... integers? Also, when you say irreducible, you have to specify irreducible over what. No polynomial with integer coefficients is irreducible over the complex numbers, but might be irreducible over, say, the reals or the rational numbers.

Petek

 

[danieldf]

Oh really.. Sorry, i just forgot that.
They're integers (naturals in fact)
And i mean irreducible over rationals.

Thx!