Lesson 5: Polynomial Long Division

Lesson 5: Polynomial Long Division

To begin the lesson, click the Lesson Pages button to print them.

Objectives


  • Simplify expressions by dividing a polynomial by a monomial.
  • Use long division to divide polynomials.
  • Write the remainder of a polynomial expression as a rational expression.

Why?


Polynomial long division is useful when a polynomial needs to be broken down into smaller parts. It is also used in some forms of computer programming, such as error-control coding and cyclic redundancy check (CRC) methods.

The Warm Up activates prior knowledge that is related and important to your understanding of the lesson. It is a great way to prepare your mind for what you are about to learn.

Find the Warm Up in your lesson pages.
Follow the instructions to complete it.

In Explore you will watch videos based on the objectives for this lesson. As you watch the videos, complete the notes and examples in your lesson pages. At the end of each topic, you will find a Checkpoint problem to complete.

To get started, click each topic below in order.


Click    to watch each video.
Fill in the notes and examples in your lesson pages as you watch the videos.

Dividing by a Monomial

Example 1

Example 2

Checkpoint: Dividing by a Monomial

Now it’s your turn! A Checkpoint is an opportunity to complete a problem on your own using what you have learned.

Complete the Checkpoint for this topic in your lesson pages.

Check in with your instructor after completing the Checkpoint.

Click    to watch each video.
Fill in the notes and examples in your lesson pages as you watch the videos.

Polynomial Long Division to Factor (No Remainders)

Example 3

Example 4

Example 5

Example 6

Checkpoint: Polynomial Long Division to Factor (no remainders)

Now it’s your turn! A Checkpoint is an opportunity to complete a problem on your own using what you have learned.

Complete the Checkpoint for this topic in your lesson pages.

Check in with your instructor after completing the Checkpoint.

Click    to watch each video.
Fill in the notes and examples in your lesson pages as you watch the videos.

Polynomial Long Division with Remainders

Example 7

Polynomial Long Division with Remainders (cont.)

Example 8

Example 9

Checkpoint: Polynomial Long Division with Remainders

Now it’s your turn! A Checkpoint is an opportunity to complete a problem on your own using what you have learned.

Complete the Checkpoint for this topic in your lesson pages.

Check in with your instructor after completing the Checkpoint.

Practice 1

Now that you have finished exploring, it’s time to apply and practice what you have learned. Remember to have your Formula Sheet and a calculator handy.

Complete Practice 1 in your lesson pages.

After completing Practice 1, check in with your instructor to determine if you should go to the Mastery Check or Practice 2.

Practice 2

Do you need more practice? With your instructor, decide if you would benefit from more practice based on your comfort level with Practice 1 and/or the Mastery Check.

Complete Practice 2 in your lesson pages.

After completing Practice 2, check in with your instructor.

The Mastery Check is a multifaceted problem that helps determine if you have mastered the lesson objectives.

Complete the Mastery Check in your lesson pages.
Self-evaluate your work using the Mastery Check Rubric.

After completing the Mastery Check and your self-evaluation, check in with your instructor.

In the Targeted Review, you will practice topics you have mastered in earlier lessons or levels. Reviewing these concepts will help you be successful as you work through this unit.

Complete the Targeted Review in your lesson pages.

After completing the Targeted Review, check in with your instructor.

More to Explore is an opportunity to grow and challenge your knowledge and understanding of what you have learned in the lesson. Carefully read and follow the instructions as the activity formats vary from lesson to lesson.

  • Build the quadratic expression to find the binomial factors.
  • List the polynomial as the product of binomial factors.

Then complete the long division problem.

Problem 1 has been completed for you as an example.

1) x+2x2+7x+10

x2+7x+10x+2x+5

x+2x+5x2+7x+10(x2+2x)5x+10(5x+10)0

2) x+1x2+7x+6

3) x+3x2+8x+15

4) 2x+14x2+4x+1

5) 2x+14x2+10x+4