Consider: "Let $K$ be a field. Then every polynomial $p\in K[X]$ is transcendent over $K$." My question are:
1) How can polynomial be transcendent over something ? I thought that definition applied only for elements of $K$...
2) How can I show the above ? Do I have to find a polynomial "whose coefficients are polynomials" such that $p$ is the root of this greater polynomial ?