Definition:Constant Polynomial

Definition

Let $R$ be a commutative ring with unity.

Let $P \in R \left[{x}\right]$ be a polynomial in one variable over $R$.

Definition 1

The polynomial $P$ is a constant polynomial if and only if its coefficients of $x^k$ are zero for $k \ge 1$.

Definition 2

The polynomial $P$ is a constant polynomial if and only if $P$ is either the zero polynomial or has degree $0$.

Definition 3

The polynomial $P$ is a constant polynomial if and only if it is in the image of the canonical embedding $R \to R \sqbrk x$.

Nonconstant Polynomial

Let $R$ be a commutative ring with unity.

Let $P \in R \left[{x}\right]$ be a polynomial in one variable over $R$.

The polynomial $P$ is a nonconstant polynomial if and only if $P$ is not a constant polynomial

Also see

• Equivalence of Definitions of Constant Polynomial