Can a polynomial have an irrational coefficient?

[Prof B]

In general, given a field, $F$, you can talk about "polynomials over the field $F$" when the coefficients are required to be in the field $F$

The integers are not a field. But the integers are a ring, and you can talk about polynomials over any ring. If you don't know which ring from context, it is a good idea to ask. One reason teachers ask questions like the OP's is to find out whether you know which ring.

 

[FactChecker]

The integers are not a field. But the integers are a ring, and you can talk about polynomials over any ring. If you don't know which ring from context, it is a good idea to ask. One reason teachers ask questions like the OP's is to find out whether you know which ring.

Good point. I stand corrected.