## Synthetic Division- Let's do it the easy way - Section 4: Comparing Long and Synthetic Division

*Synthetic Division- Let's do it the easy way*

*Synthetic Division- Let's do it the easy way*

# Synthetic Division

Lesson 2 of 15

## Objective: Students will be able to divide polynomials using synthetic division.

#### Warm Up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Synthetic Divison, which asks students to determine which of two methods of graphing a shrink of ½ on a quadratic function is correct.

I also use this time to correct and record the previous day's Homework.

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We start this lesson with a polynomial long division problem. I ask the students to work on it by themselves and we go over it together. We then go over the same problem with synthetic division.

Next, I have the students watch a video, from Khan Academy, that explains WHY synthetic division works. The explanation is very well done. A good potential enrichment activity would be to set the students to explaining why it works either after watching the video or without it at all (**Math Practice 3**).

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The remainder of the lesson is Guided Practice on synthetic division. I often ask the students to attempt a problem and then we discuss the reason students may be getting different solutions. I also have pairs of students check each other’s work as a strategy for avoiding student mistakes.

Once, we reach a problem whose divisor has a leading coefficient greater than one, I give them some time to work on the problem with no introduction. We stop and discuss how to deal with this problem.

The final problem has a divisor that is a trinomial. Again, I give the students this problem with little introduction. After they have had a chance to puzzle over it, I ask the students if they have any concerns (**Math Practice 1**). This should hopefully lead to a discussion on how to represent a trinomial as a zero which leads to the fact that synthetic division isn't useful for problems like these.

Please see the PowerPoint for detailed presentation notes.

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The final task in this lesson asks students “When is it best to use synthetic division and when is it best to use regular long division?” (**Math Practice 5**) I would use a think-pair-share with this one. This should firm up and bring together the last two lessons.

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#### Homework Assignment

*1 min*

This Homework gives students some practice with synthetic division. The final question is a critical thinking problem that can be used as enrichment. I have included an alternate assignment with the final enrichment problem added.

This assignment was created with Kuta Software which is a great resource for secondary mathematics teachers.

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket offers the same problem as the previous lesson only students are to complete the problem with synthetic rather than long division.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Polynomial Long Division
- LESSON 2: Synthetic Division
- LESSON 3: Uses of Polynomial Division- The Factor and Remainder Theorems
- LESSON 4: Introduction to Polynomial Equations
- LESSON 5: Solving Polynomial Equations Graphically
- LESSON 6: Graphs of Polynomial Functions
- LESSON 7: Intercepts of Polynomial Functions
- LESSON 8: Solving Polynomial Equations Day 1
- LESSON 9: Solving Polynomial Equations Day 2
- LESSON 10: Transformation of Polynomial Functions
- LESSON 11: Modeling Volume with Polynomials Day 1
- LESSON 12: Modeling Volume with Polynomials Day 2
- LESSON 13: Polynomial Functions Review Day 1
- LESSON 14: Polynomial Functions Review Day 2
- LESSON 15: Polynomial Functions Test