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# Long, Synthetic, and Square! Oh my! Polynomial Division

Lesson 8 of 15

## Objective: SWBAT divide polynomials using a variety of methods.

## Big Idea: This teacher-led lesson demonstrates various forms of polynomial division: long division, synthetic division, and polynomial division using generic squares.

*41 minutes*

#### Warm-up: Long Division

*5 min*

**Environment: **Today’s lesson is very teacher-driven. So the grouping of students does not matter today. Students should be ready to take notes during class and ask questions if they have them as today’s lesson is very skilled based. Also, I will not be having students log in to their clickers (personal response systems) today as I find it too difficult to do quick polls when working in a PowerPoint. I hate how it closes you out of power point view mode to be able to poll. So today, my students will get off the hook with texting in answers; but will of course still be required to practice the problems on paper.

**Narrative: **Give students an opportunity to recall how to do long division. Have students complete the problem on the first slide of the PowerPoint. In the past, it has really made students have to stop and think as they haven’t done long division in quite some time. It is important that students recall the procedure for how to long divide with constants as they will be required to do the division algorithm soon with polynomials. I plan to go over the warm-up step-by-step just to insure that every student in the class is able to recall how to do long division.

**Differentiation: **I have found in the past that students claim they never learned long division. I am sure it was taught somewhere along the lines, but some students never mastered it and/or never retained how to do it. I like to have some basic division worksheets on hand during my Advisory period that day and request students who have either told me they don’t know how to long divide or who have shown they were not successful with the warm-up. I think it is essential that students learn to be able to divide polynomials using long division as it always works! Synthetic division is a short-cut. And dividing using generic squares doesn’t really build on prior knowledge like ling division so I think it will be quickly forgotten by students. I think it is important for students to master long division with numbers before they try to tackle polynomial division.

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Puzzling Polynomials and Quizzical Quadratics
- LESSON 2: Building Connections: Building Polynomials (Day 1 of 2)
- LESSON 3: Building Connections: Building Polynomials (Day 2 of 2)
- LESSON 4: Detailed Descriptions of our Puzzling Polynomials
- LESSON 5: Got zeros? Polynomials do! Multiplicity of Zeros (Day 1 of 3)
- LESSON 6: Got zeros? Polynomials do! Multiplicity of Zeros (Day 2 of 3)
- LESSON 7: Got zeros? Polynomials do! Multiplicity of Zeros (Day 3 of 3)
- LESSON 8: Long, Synthetic, and Square! Oh my! Polynomial Division
- LESSON 9: Rational Roots and Remainders: Important Theorems of Polynomials
- LESSON 10: Polynomials with Complexes… Complex Zeros that is!
- LESSON 11: Putting the Pieces of Polynomials Together (Day 1 of 2)
- LESSON 12: Putting the Pieces of Polynomials Together (Day 2 of 2)
- LESSON 13: Roller Coaster Polynomials
- LESSON 14: Test Review
- LESSON 15: Polynomials Unit Test