Polynomial

A polynomial $P$ over a commutative ring $A$ is a finite sequence $(a_i)_i$ in $A$. Most of the time, we write it this way
$$P=\sum_{i=0}^n a_i X^i=a_0+a_1 X+a_2 X^2+\cdots+a_n X^n$$where $X$ is called a "formal variable" and $n$ is the biggest integer $k$ such that $a_{k}\neq 0$.

Remarks

• $n$ is called the degree of $P$.
• The set of all polynomials in $X$ with coefficients in $A$ is denoted $A[X]$.