Definition:Content of Polynomial

Integer Polynomial
Let $f \in \Z \sqbrk X$ be a polynomial.

Then the content of $f$, denoted $\cont f$, is the greatest common divisor of the coefficients of $f$.

Rational Polynomial
If $f \in \Q \sqbrk X$ then there is some $n \in \N$ such that $n f \in \Z \sqbrk X$.

Then we define the content of $f$ to be:
 * $\cont f := \dfrac {\cont {n f} } n$

Polynomial over GCD Domain
Let $D$ be a GCD domain.

Let $K$ be the quotient field of $D$.

Let $f \in K \sqbrk X$ be a polynomial.

Let $a \in D$ be such that $a f \in D \sqbrk X$.

Let $d$ be the greatest common divisor of the coefficients of $a f$.

Then we define the content of $f$ to be:
 * $\cont f := \dfrac d a$

General ring with unity
Let $R$ be a commutative ring with unity.

Let $f \in R \sqbrk X$ be a polynomial.

The content of $f$ is the ideal generated by its coefficients.

Also see

 * Content of Polynomial over UFD is Well Defined
 * Content of Polynomial is Multiplicative
 * Definition:Primitive Polynomial: A polynomial $f$ is primitive if $\cont f = 1$.