Definition:Constant Term of Polynomial

Definition

Let $R$ be a commutative ring with unity.

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

$\ds f = \sum_{k \mathop = 0}^n a_k \circ x^k$

where $n$ is the degree of $P$.

The constant term of $P$ is the coefficient $a_0$ of $x^0$.

Examples

Arbitrary Example $1$

The constant term of the polynomial:

$x^3 - 6 x + 2$

is $2$.

Arbitrary Example $2$

The constant term of the polynomial:

$x^4 + 2 x^3 - x$

is $0$.

Also see

• Results about constant terms of polynomials can be found here.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $9$: Rings: Exercise $21$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): constant term
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): constant term
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polynomial