Q:

The field of rational polynomials?

So I was looking across the definition for irreducible polynomials on Wolfram Mathworld when I came across this:

For example, in the field of rational polynomials $\mathbb{Q}[x]$...

But I feel that there's no such field? Polynomials can't form a field, can they? I just want to make sure.

A:

This just terminology, but $\mathbb{Q}[x]$ denotes the ring of all polynomials with coefficients in the rational numbers. 
This has a fraction field, consisting of all quotients of such functions, which is what I assume the quote refers to. This is the field of elements of the form $\frac{p(x)}{q(x)}$, where $p$ and $q$ are rational polynomials as above. This is sometimes denoted by $\mathbb{Q}(x)$. We use square brackets to enlarge something as a ring, i.e. admitting sums and powers of the thing, and we use parentheses to extend something as a field. These are of course very different in general.

