Types of Polynomials

Monomials

A monomial is an expression with one term.  However, the term can not have a variable in its denominator.

Examples:  

bullet-5
bullet 4x
bullet3
bullet-10xy

Binomials

A binomial is a polynomial with two terms.

Examples:  

bullet6x + 3
bullet-12x - 3y, 7xy + z

Trinomials

A trinomial is a polynomial with three terms.

Examples:  

bullet6x2 + 3x + 5
bullet-2xy + 3x - 5z

 

Other Special Notes About Polynomials

Degree

The degree of a monomial is the sum of the exponents of its variables.

Examples:

bullet-5 has degree = 0 (because it has no variables)
bullet6x2 has degree = 2
bullet6x2y has degree = 3 (because the exponent on y is 1, we just don't write it)

 

The degree of a polynomial is the highest degree of any of its terms, after it has been simplified.  (i.e. like terms have been combined)

Examples:

bullet6x2 + 3x + 5 has degree = 2 (because 6x2 has the highest degree)
bullet-5x + 6x2y + 7x -6x2y + 5xy simplifies to -5x + 7x + 5xy so the polynomial has degree = 2 (because the degree of 5xy is 2)