Polynomial
Let \(R\) be a ring , and \(x\) an indeterminate. We define a polynomial in \(x\), over \(R\) to be an expression of the form:
\[ f(x)=a_0+a+1x+\dots+a_nx^n \]for some integer \(n \in \Z^+\), and where \(a_0, \dots, a_n \in R\).
(sidenote: In most cases, the indeterminate \(x\) is understood and so we omit any explicit mention to it most of the time. )