Dividing a Polynomial by a Monomial

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

In this lesson, learn about polynomials and monomials and the 3 simple steps you can use to divide a polynomial by a monomial. Then, you will get a chance to practice it yourself!

What is a monomial?

Before we can think about dividing polynomials and monomials, we have to know what they are! How can you tell if something is a monomial? The prefix mono always means one, so a monomial is a mathematical expression with just one term. That term can include numbers (like 1, 4, or -12), and variables (like a, b, x, y, z, or even a2 ). It can even include more than one variable, as long as those variables are all multiplied together. Take a look at the following terms and see if you can tell which ones are monomials.

examples of monomials

What is a polynomial?

So, if a monomial is a mathematical expression with just one term, what is a polynomial? Poly always means many, so a polynomial is a mathematical expression with more than one term. It can have 2 terms, or 3, 10, 20, or even more! Anything with more than one term is a polynomial. Here are some examples of polynomials:

examples of polynomials

How to divide a polynomial by a monomial

To divide a polynomial by a monomial, you need to follow these three simple steps:

Step 1: Rewrite the problem and divide EACH term in the polynomial by the monomial.

step 1

Step 2: Divide the numbers. Do not do anything with the variables yet. We'll get to that in a minute!

step 2

Step 3: Now divide the variables. When you divide 2 variables, look at the exponents of each and subtract the exponent of the variable in the numerator, the top number in the fraction, from the exponent of the variable in the denominator, the bottom number in the fraction. For example a5 divided by a2 would be a(5-2) or a3

step 3

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