Divide and Conquer: Mastering Polynomial Long Division

Algebra 2 Grades High School 10:11 Video
Print Lesson Plan Watch Video

Lesson Description

Learn the process of polynomial long division, including how to handle remainders, with clear examples and step-by-step instructions. This lesson builds upon previous algebra knowledge and prepares students for more advanced polynomial operations.

Video Resource

Polynomial Long Division | With Remainder

Kevinmathscience

Duration: 10:11
Watch on YouTube

Key Concepts

  • Polynomial Long Division Algorithm
  • Identifying Dividend, Divisor, Quotient, and Remainder
  • Handling Remainders in Polynomial Division

Learning Objectives

  • Students will be able to perform polynomial long division with and without remainders.
  • Students will be able to correctly express the quotient and remainder in the appropriate format.
  • Students will be able to apply polynomial long division to solve related algebraic problems.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic division concepts and their relationship to polynomial expressions. Briefly discuss the difference between polynomial division with and without remainders. Show the video to the class.
  • Step-by-Step Example Walkthrough (15 mins)
    Go through the first example from the video, pausing at each step to explain the logic and math involved. Emphasize the importance of aligning terms, changing signs, and bringing down the next term. Address any student questions or confusion.
  • Guided Practice (15 mins)
    Work through the second example from the video as a class, having students actively participate in each step. Encourage students to verbalize their understanding of the process. Provide immediate feedback and corrections.
  • Independent Practice (15 mins)
    Assign practice problems for students to solve individually. These problems should vary in complexity, including cases with and without remainders. Monitor student progress and provide assistance as needed.
  • Wrap-up and Assessment (10 mins)
    Review the key concepts and steps of polynomial long division. Administer a short quiz to assess student understanding. Preview upcoming topics related to polynomial functions.

Interactive Exercises

  • Polynomial Division Matching
    Provide students with a set of polynomial division problems and a set of solutions (quotients and remainders). Students must match each problem with its correct solution.

Discussion Questions

  • How is polynomial long division similar to/different from numerical long division?
  • What are the potential errors students might make and how can they be avoided?
  • How can polynomial long division be used to solve real-world problems?

Skills Developed

  • Algebraic Manipulation
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

What is the first step in polynomial long division?

Correct Answer: Divide the leading term of the dividend by the leading term of the divisor.

Question 2:

When do you know you've reached the remainder in polynomial long division?

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

Question 3:

In polynomial long division, what operation is performed after multiplying the quotient term by the divisor?

Correct Answer: Subtraction

Question 4:

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

Correct Answer: 0

Question 5:

Which of the following represents the correct way to write the final answer with a remainder 'r' and divisor 'd'?

Correct Answer: Quotient + r/d

Question 6:

When dividing (2x^3 - 5x^2 + 3x - 1) by (x-2), what is the degree of the quotient?

Correct Answer: 2

Question 7:

What should you do if a term is missing in the dividend (e.g., no x term)?

Correct Answer: Insert a zero as a placeholder for the missing term.

Question 8:

The polynomial division (x^3 + 8) / (x + 2) results in a remainder of 0. What does this tell us about (x+2)?

Correct Answer: It is a factor of (x^3 + 8).

Question 9:

What is the quotient when 6x^2 + 5x - 6 is divided by 2x + 3?

Correct Answer: 3x - 2

Question 10:

If a polynomial is divided by (x-a) and the remainder is 0, then what is 'a'?

Correct Answer: A root of the polynomial

Fill in the Blank Questions

Question 1:

The polynomial being divided is called the ________.

Correct Answer: dividend

Question 2:

The polynomial you are dividing by is called the ________.

Correct Answer: divisor

Question 3:

The result of the polynomial division (without the remainder) is called the ________.

Correct Answer: quotient

Question 4:

The part left over after polynomial division, if any, is called the ________.

Correct Answer: remainder

Question 5:

Before starting polynomial long division, make sure the polynomials are written in ________ order of exponents.

Correct Answer: descending

Question 6:

When a term is missing in the dividend, you should use a ________ as a placeholder.

Correct Answer: zero

Question 7:

To check your answer after polynomial long division, multiply the divisor by the ________ and add the remainder.

Correct Answer: quotient

Question 8:

If the remainder is 0, the divisor is a ________ of the dividend.

Correct Answer: factor

Question 9:

The degree of the remainder must be ________ than the degree of the divisor.

Correct Answer: less

Question 10:

In the final answer, the remainder is written as a fraction with the remainder over the ________.

Correct Answer: divisor

Educational Standards

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

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans