Subtracting Polynomials: Examples & Concept

Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

A polynomial is an expression containing variables and constants. This lesson will cover how to subtract one polynomial from another, which requires careful mathematical attention. A quiz will give you the opportunity to practice this skill.

What is a Polynomial?

A polynomial is an expression of determined length that contains constants (numbers) and variables (letters). Each term of the polynomial will have a different exponent. The prefix 'poly' means 'many,' and 'nomial' means 'terms'; however, polynomials can have multiple terms or only one term. There are some expressions that might look like polynomials but are actually not; any terms with either a negative exponent or a fraction with the variable in the denominator are not polynomials and are treated differently, in a mathematical sense.


Polynomials have a wide range of applications in math and science. They're used to form polynomial equations, which are mathematical representations of everything from simple word problems to complex applications in the sciences.

Examples of Polynomials

The Trouble with Polynomials

Most of the same mathematical operations that can be done with numbers, such as addition, subtraction, multiplication and division, can also be performed with polynomials. Subtracting polynomials can be difficult. It's important to keep track of the positive and negative signs that correspond with each term. Subtracting negatives can get tricky, especially when you're working with multiple terms. It is also critical to keep like terms - those terms with the same variable (including exponents) - together.

Subtracting Polynomials

There are two ways to subtract polynomials. Both of them work equally well, and the method you choose will depend on which one works best for you.

The first method, called the vertical method, requires setting up your subtraction problem just like a problem involving large numbers - write the polynomial you're going to subtract underneath the first polynomial. Remember to match up like terms. Like terms are terms that have the same variables and exponents but different coefficients (the number in front of the variable).


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