Dividing Polynomials Worksheets

Free Dividing Polynomials Worksheet Library (Answer Keys Included)

Are you looking for a Dividing Polynomials Worksheet to help your students gain some extra practice and experience with this challenging algebra skill?

If so, then you are in the right place! This page shares a 100% free Dividing Polynomials Worksheet Library where you can download a handful of free and printable PDF practice worksheets. Each worksheet includes 16-24 unique practice problems along with a complete answer key.

Any of our dividing polynomials worksheets can be downloaded simply by clicking on any of the text links included in the worksheet library in the section below. Clicking on any of the text links will open the preview window for that particular worksheet. From the preview page, you will have the option to save the worksheet PDF file to your computer or to print the worksheet with our without the included answer key. You will also have the option to print each worksheet in color or in grayscale.

Just below the dividing polynomials worksheet library, you will find a review section that includes a step-by-step explanation of how to solve different types of dividing polynomials practice problems (including dividing polynomials by monomials and dividing polynomials by polynomials). If you are struggling to solve problems on any dividing polynomials worksheet, then we highly recommend that you visit this section.

Finally, the free worksheets shared in the library below are all sample activities from the Mashup Math K-12 Infinite Worksheet Libraries, which offer hundreds of free PDF math worksheets and answer keys for students in grades K-12 and beyond. | Quick Guide: How to Download/Print

Dividing Polynomials Worksheet Library

▶️ Dividing Polynomials Practice (A)

▶️ Dividing Polynomials Practice (B)

▶️ Extended Practice: Dividing Polynomials

Are You Looking for More FREE Math Worksheets?👀

If so, be sure visit the Mashup Math Infinite Worksheets Library, where you can download hundreds of PDF practice worksheets and activities answer keys for Grades K-12, Algebra, and Geometry topics!

Dividing Polynomials Worksheet Review

Are you struggling with any of the problems on a dividing polynomials worksheet, then this section will serve as a helpful review of some key points related to dividing polynomials, including a few step-by-step examples.

In math, dividing polynomials is when you take a complex algebraic expression with two or more terms and break it down into a smaller and simpler expression with one or more terms.

For example, lets’ solve the following dividing polynomials problem:

Dividing Polynomials Worksheet Example #1

Solve: (6x²+12x) ÷ 3x

For this first example, we have to divide the binomial 6x²+12x by the monomial 3x.

Our first step is to divide each term of the binomial, 6x²+12x, by the monomial 3x as follows:

• (6x²)/3x = 2x

• (12x)/3x = 4

Next, we can take both results and write them as an expression that represents the quotient:

• (6x²+12x) ÷ 3x = 2x + 4

Finally, you can check your answer by taking the results, 2x + 4, and multiplying it by the divisor, 3x, to see if the result is the dividend:

• 3x(2x+4) = 6x² + 12x ✓

Since our answer checks out, we can conclude that the final answer is 2x + 4.

The complete step-by-step process for solving this first example is shown in Figure 01 below.

Now, let’s look at a more complex example where we have to divide a trinomial by a binomial.

Dividing Polynomials Worksheet Example #2

Solve: (x³ + 3x² + 3x + 1) ÷ (x+1)

While this next example is more complex than the previous example, our approach for solving this problem is still the same.

We can start by dividing the first terms as follows:

• x³ ÷ x = x²

Next, we have to multiply the divisor, (x+1), by our result, x², as follows:

• (x+1)(x²) = x³ + x²

From here, we have to subtract our result from the previous step from the polynomial that we are dividing:

• (x³ + 3x² + 3x + 1) - (x³ + x²) = 2x² +3x + 1

Now we can repeat this process again using the second term as follows:

• 2x² ÷ x = 2x

Then, perform multiplication as follows:

• (x + 1)(2x) = 2x² + 2x

Next, perform subtraction as follows:

• 2x² +3x + 1 - (2x² + 2x) = x + 1

And we can continue this process until we end up with a remainder of zero:

• x ÷ x = 1

• (x + 1)(1) = x + 1

• (x + 1) - (x + 1) = 0

Now that we have a remainder of 0, we have solved the problem and we can conclude that the the final answer is x² + 2x + 1.

All of the steps that we used to solve this second example are illustrated in Figure 02 below.