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Monomials, Binomials, Polynomials

A monomial is any product of numbers and variables, like $17$ , or $3xy$ , or $-4x^2$ , 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 $55x^2-33y^2$ 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.