Monomial
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Definition
A monomial[1] is a a polynomial consisting of "no [ilmath]+[/ilmath] sign" if you will (unless it is in the coefficient), for example:
- [ilmath]12xy^2z[/ilmath] is a monomial
- [ilmath](12+2j)xy^2z[/ilmath] is also a monomial (just over the complex numbers)
In short, it is a polynomial of just one term.
Properties
- The degree[1] of a monomial is the sum of the powers involved.
- For example [ilmath]xy^2z[/ilmath] is of degree [ilmath]4[/ilmath]
First theorems
Theorem: There are [ilmath]{}^{n+k-1}C_n[/ilmath] monomials of degree [ilmath]n[/ilmath] in the [ilmath]k[/ilmath] variables [ilmath]x_1,x_2,\cdots,x_k[/ilmath]
