sage: x = polygen(ZZ)
sage: f = 2*x^2
sage: f.mod(2)==0
False
sage: type(f.mod(2))
<type
'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>

Even this doesn't work:
sage: R.<x> = ZZ[]
sage: f.mod(2*R)==0
False

But last I checked, 2 | 2x^2.
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