Mastering Polynomial Long Division: Tips and Techniques

Algebra 2 Grades High School 10:54 Video
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Lesson Description

Learn the ins and outs of polynomial long division with helpful tips and techniques to simplify the process. This lesson covers setting up the problem, handling missing terms, and interpreting remainders.

Video Resource

Polynomial Long Division (Tips and Techniques)

Mario's Math Tutoring

Duration: 10:54
Watch on YouTube

Key Concepts

  • Polynomial long division
  • Placeholders for missing terms
  • Remainder Theorem

Learning Objectives

  • Students will be able to correctly set up and perform polynomial long division.
  • Students will be able to identify and use placeholders for missing terms in polynomials.
  • Students will be able to express the result of polynomial long division with the remainder in the correct form.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of long division with numerical examples. Connect this to polynomial division, highlighting the similarities in the process.
  • Video Instruction (15 mins)
    Watch the YouTube video 'Polynomial Long Division (Tips and Techniques)' by Mario's Math Tutoring. Encourage students to take notes on the key steps and techniques presented.
  • Guided Practice (20 mins)
    Work through example problems similar to those in the video, emphasizing the importance of placeholders for missing terms. Guide students through each step, explaining the reasoning behind it.
  • Independent Practice (15 mins)
    Have students work on practice problems independently. Circulate to provide assistance and address any questions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and address any remaining questions. Administer the multiple-choice and fill-in-the-blank quizzes to assess understanding.

Interactive Exercises

  • Error Analysis
    Present students with worked-out problems containing common errors in polynomial long division. Have them identify and correct the errors.
  • Partner Practice
    Have students work in pairs to solve polynomial long division problems, taking turns explaining each step to their partner.

Discussion Questions

  • Why is it important to use placeholders for missing terms in polynomial long division?
  • How is polynomial long division similar to regular long division with numbers?
  • How can you check your answer after performing polynomial long division?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in polynomial long division?

Correct Answer: Set up the division problem.

Question 2:

Why are placeholders (zero terms) important in polynomial long division?

Correct Answer: They ensure terms are aligned correctly.

Question 3:

When do you stop the long division process?

Correct Answer: When the degree of the remainder is less than the degree of the divisor.

Question 4:

What do you do with the remainder after polynomial long division?

Correct Answer: Write it as a fraction over the divisor.

Question 5:

If dividing (x^3 + 2x - 1) by (x + 1), what placeholder do you need?

Correct Answer: 0x^2

Question 6:

What is the degree of the remainder always in comparison to the divisor?

Correct Answer: Lower

Question 7:

Which of the following represents the correct setup for (2x^4-3x+1) / (x^2+1)?

Correct Answer: (x^2+0x+1) / (2x^4+0x^3+0x^2-3x+1)

Question 8:

What is the quotient when (x^2 - 5x + 6) is divided by (x - 2)?

Correct Answer: x - 3

Question 9:

What is the divisor in the problem (x^3 + 4x^2 - 3x + 2) / (x - 1)?

Correct Answer: x - 1

Question 10:

The result of dividing (x^2 + 7x + 12) by (x + 3) is (x + 4) with no remainder. This means (x+3) is a ______ of (x^2 + 7x + 12)

Correct Answer: factor

Fill in the Blank Questions

Question 1:

When a polynomial is missing a term, we insert a ______ as a placeholder.

Correct Answer: zero

Question 2:

The expression being divided is called the ______.

Correct Answer: dividend

Question 3:

The expression we are dividing by is called the ______.

Correct Answer: divisor

Question 4:

The result of the division, excluding the remainder, is called the ______.

Correct Answer: quotient

Question 5:

The expression left over after the division process is complete is called the ______.

Correct Answer: remainder

Question 6:

In polynomial long division, you should continue dividing until the degree of the remainder is ______ than the degree of the divisor.

Correct Answer: less

Question 7:

If you are missing an x term when you have terms for x^2 and a constant, the placeholder term would be ______.

Correct Answer: 0x

Question 8:

If the remainder is 0, that means the divisor is a ______ of the dividend.

Correct Answer: factor

Question 9:

The process of using polynomial long division can also be used to determine any _______ of a polynomial.

Correct Answer: roots

Question 10:

What is the constant term of x^4 +3x^2 +7

Correct Answer: 7

Educational Standards

A2.A.2.2:Add, subtract, multiply, divide, and simplify polynomial expressions. A2.A.1.4:Solve polynomial equations with real roots using various methods (e.g., polynomial division, synthetic division, using graphing calculators or other appropriate technology).

Teaching Materials

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