# Definition:Constant Polynomial

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## 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 $R \to R \left[{x}\right]$.