tests whether poly is an irreducible polynomial over the rationals.

IrreduciblePolynomialQ[poly, Modulus->p]
tests whether poly is irreducible modulo a prime p.

IrreduciblePolynomialQ[poly, Extension->{a1, a2, ...}]
tests whether poly is irreducible over the field extension generated by the algebraic numbers .

IrreduciblePolynomialQ[poly, Extension->All]
tests whether poly is absolutely irreducible over the complex numbers.

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