The problem isn't with Optional but with the fact that Plus will evaluate pattern sequences as in _ + _ to get unpleasant results like 2 _. In your pattern, you can prevent this by simply wrapping everything in HoldPattern:

Clear[intPolyQ] intPolyQ[HoldPattern[ Optional[_Integer] + Plus[Optional[_Integer] x_Symbol^Optional[_Integer] ...]], x_] := True; intPolyQ[___] := False; 

With this, the function seems to work fine:

intPolyQ[#, x] & /@ {x, 2 x, 2 x + 1, 2 x^2 + 3 x, 2 x^2 + 3 x + 1} (* ==> {True, True, True, True, True} *) 

Of course there is also an easier way to test for integer polynomials - let's call the polynomial poly, then you could just do

And @@ IntegerQ /@ CoefficientList[poly] 

The problem isn't with Optional but with the fact that Plus will evaluate pattern sequences as in _ + _ to get unpleasant results like 2 _. In your pattern, you can prevent this by simply wrapping everything in HoldPattern:

intPolyQ[HoldPattern[ Optional[_Integer] + Plus[Optional[_Integer] x_Symbol^Optional[_Integer] ...]], x_] := True; intPolyQ[___] := False; 

With this, the function seems to work fine if you also retain your old definitions as @kguler observed:

intPolyQ[#, x] & /@ {x, 2 x, 2 x + 1, 2 x^2 + 3 x, 2 x^2 + 3 x + 1} (* ==> {True, True, True, True, True} *) 

Of course there is also an easier way to test for integer polynomials - let's call the polynomial poly, then you could just do

And @@ IntegerQ /@ CoefficientList[poly]