Summary: Defining Polynomials

In this section, we have learned the definition of a polynomial, how to evaluate a polynomial, and how to classify a polynomial according to the number of its terms and the degree of its highest exponent.

How to identify the degree and leading coefficient of a polynomial expression

  1. Find the highest power of the variable (usually x) to determine the degree.
  2. Identify the term containing the highest power of the variable to find the leading term.
  3. Identify the coefficient of the leading term.

Degree of a Polynomial

  • The degree of a term is the exponent of its variable.
  • The degree of a constant is [latex]0[/latex].
  • The degree of a polynomial is the highest degree of all its terms.


  • Polynomial Algebraic expression that is created by combining numbers and variables using arithmetic operations such as addition, subtraction, multiplication, division, and exponentiation.
  • Monomial  The basic building block of a polynomial. [latex]a{x}^{m}[/latex], where [latex]a[/latex] is a constant and [latex]m[/latex] is a whole number.  A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent.
  • Binomial  A polynomial containing exactly two terms.
  • Trinomial  A polynomial containing exactly three terms.
  • Coefficient  The number part of a term.
  • Leading term  The term with the highest degree.
  • Leading coefficient  The coefficient of the term with the highest degree.
  • Standard form  When the terms of the polynomial are arranged from the highest degree to the lowest degree.