code: def test_dup_zz_irreducible_p():
      R, x = ring("x", ZZ)
  
      assert (
          R.dup_zz_irreducible_p(
              3 * x**4 + 2 * x**3 + 6 * x**2 + 8 * x + 7
          )
          is None
      )
      assert (
          R.dup_zz_irreducible_p(
              3 * x**4 + 2 * x**3 + 6 * x**2 + 8 * x + 4
          )
          is None
      )
  
      assert (
          R.dup_zz_irreducible_p(
              3 * x**4 + 2 * x**3 + 6 * x**2 + 8 * x + 10
          )
          is True
      )
      assert (
          R.dup_zz_irreducible_p(
              3 * x**4 + 2 * x**3 + 6 * x**2 + 8 * x + 14
          )
          is True
      )
  
imports: from sympy.polys.rings import ring, xring
  from sympy.polys.domains import FF, ZZ, QQ, ZZ_I, QQ_I, RR, EX
  from sympy.polys import polyconfig
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.polyclasses import ANP
  from sympy.polys.specialpolys import f_polys, w_polys
  from sympy.core.numbers import I
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import sin
  from sympy.ntheory.generate import nextprime
  from sympy.testing.pytest import raises, XFAIL
label_desc: Use image node_id 7 for calling a global function with example usage: test_dup_zz_irreducible_p() without return types