Lesson 1: Adding and Subtracting Polynomials

Property

A polynomial is an algebraic expression with several terms. Each term is a power of a variable (or a product of powers) with a constant coefficient.
The exponents in a polynomial must be whole numbers, which means that a polynomial has no radicals containing variables, and no variables in the denominators of fractions.

Examples

• The expression $4x^3 + 2x^2 - 7x + 5$ is a polynomial.

• The expression $2 + \frac{6}{x}$ is not a polynomial because a variable appears in the denominator.

Property

A monomial is a term of the form $ax^m$, where $a$ is a constant and $m$ is a whole number.
A monomial, or two or more monomials combined by addition or subtraction, is a polynomial.
A polynomial with exactly one term is called a monomial.
A polynomial with exactly two terms is called a binomial.
A polynomial with exactly three terms is called a trinomial.

Examples

• $15x^4$ is a monomial because it has one term.
• $y^2 - 25$ is a binomial because it has two terms.
• $3a^2 - 6a + 9$ is a trinomial because it has three terms.

Explanation

Think of polynomials as a family. Monomials (one term), binomials (two terms), and trinomials (three terms) are specific members. We use these names for them, and call everything else with more than three terms a polynomial.