# Monomials, Binomials, Polynomials

A monomial is any product of numbers and variables, like $17$ , or $3xy$ , or $-4{x}^{2}$ , or

$\frac{\sqrt{7}}{100}{a}^{5}{b}^{6}{c}^{7}{d}^{8}{z}^{999}$

The only rules are that the variables should be raised to only positive integer powers (no square roots or $\frac{1}{x}$ 's allowed), and no plus or minus signs.

The coefficient of a monomial is the numerical part. For example, in the above examples, the coefficients are $17,3,-4$ and $\frac{\sqrt{7}}{10}$ .

A binomial is the sum of two monomials, for example $x+3$ or $55{x}^{2}-33{y}^{2}$ or

$\frac{\sqrt{7}}{100}{a}^{5}{b}^{6}{c}^{7}{d}^{8}{z}^{999}-\frac{1}{3}x$

A trinomial is the sum of three monomials.

A polynomial is the sum of $n$ monomials, for some whole number $n$ . So monomials, binomials and trinomials are all special cases of polynomials. A polynomial can have as many terms as you want.

The degree of a monomial is the sum of the exponents of all its variables. The degree of a polynomial is the term of the polynomial that has the highest degree.