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Make definition more general
Your definition of "irreducible polynomial" is for the special case
where the polynomial is defined over an extension of Q (the rationals).
At least in abstract algebra, "irreducible polynomial" often simply refers to
a polynomial that is irreducible as an element of its polynomial ring, i.e.
that can not be non-trivially factored.
Maybe you could add a note (or let me edit the entry :-) ). Something like
A polynomial f in a polynomial ring K[x] (K a field) is called irreducible iff f is an [irreducible] element of the ring K[x], i.e. f has no non-trivial
factorization over K[x].
Special case: If f has complex coefficients ...
(then the original text).
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