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## Homework Statement

Show [tex]16x^4 = 8x^3 - 16x^2 - 8x + 1[/tex] is irreducible.

## Homework Equations

Eisenstein's criteria, if there is n s.t. n does not divide the leading coefficient, divides all the other coefficients, and n^2 does not divide the last coefficient then the polynomial is irreducible (over the rationals)

## The Attempt at a Solution

I want to say that consider [tex]p'(x) = p(\frac{1}{2}x) = x^4 + x^3 - 4x^2 - 4x + 1 [/tex] is irreducible by eisenstein if we use the standard trick of substituting x+1 -> x, then we get, [tex]x^4+5x^3+5x^2-5x-5[/tex] where eisenstein is immediate. What I don't know is that if I can then say that since p' is irreducible, then p is.