Definition:Null Polynomial

One Variable
Let $R$ be a commutative ring with unity.

Let $P \in R \sqbrk X$ be a polynomial over $R$.

Definition 1
The polynomial $P$ is a zero polynomial it is the zero element of the polynomial ring $R \sqbrk X$.

Definition 2
The polynomial $P$ is a zero polynomial all its coefficients are zero.

Also known as
The null polynomial can also be referred to as the zero polynomial.

Also see

 * Equivalence of Definitions of Zero Polynomial