User:Ascii/Definition:Monomial

Definition

In elementary mathematics, a monomial is a product of:

• a number $a$ (usually from the standard number fields: $\Q$, $\R$, $\C$)

and

• a finite number of variables $x_0, \ldots, x_n$ each with respective exponents $i_0, \ldots, i_n$ from $\N_{>0}$

resulting in an expression of the form:

$a x_0^{i_0} \ldots x_n^{i_n}$

Coefficient

In the monomial:

$a x_0^{i_0} \ldots x_n^{i_n}$

$a$ is the coefficient.

Examples

Example 1: $2x$

$2x$ is a monomial where:

• $2$ is the coefficient

Example 2: $(7.4 - 3.12i)x^{13}yz^{7}$

$(7.4 - 3.12i)x^{13}yz^{7}$ is a monomial where:

• Coefficient: $7.4 - 3.12i$
• Variables: $x$, $y$, $z$
• Total degree: $21$ such that:
  • $x$ has degree $13$
  • $y$ has degree $1$
  • $z$ has degree $7$