Polynomial Long Division: Mastering the Art of Dividing Polynomials

Algebra 2 Grades High School 11:20 Video
Print Lesson Plan Watch Video

Lesson Description

Learn the step-by-step process of polynomial long division, focusing on problems with no remainders. This lesson builds essential algebraic skills for Algebra 2 students.

Video Resource

Polynomial Long Division | No Remainder

Kevinmathscience

Duration: 11:20
Watch on YouTube

Key Concepts

  • Polynomial long division algorithm
  • Dividing terms with exponents
  • Changing signs when subtracting
  • Identifying the quotient
  • Understanding no-remainder conditions

Learning Objectives

  • Students will be able to perform polynomial long division with no remainder.
  • Students will be able to identify the quotient in a polynomial long division problem.
  • Students will understand the relationship between polynomial long division and factoring.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic division concepts. Briefly introduce polynomial long division as an extension of these concepts. Show the video: Polynomial Long Division | No Remainder by Kevinmathscience. Instruct students to take notes on the steps involved.
  • Step-by-Step Breakdown (15 mins)
    Go through the first example from the video step-by-step on the board. Emphasize the following: Dividing the leading terms, Multiplying the quotient term by the divisor, Changing the signs and subtracting, Bringing down the next term, Repeating the process. Clearly explain why each step is necessary.
  • Guided Practice (15 mins)
    Work through the second example from the video, pausing at each step to ask students for input. Encourage students to explain the reasoning behind each action. Address any questions or misconceptions that arise.
  • Independent Practice (10 mins)
    Provide students with a similar polynomial long division problem to solve independently. Circulate to provide assistance as needed. Review the solution as a class.
  • Wrap-up (5 mins)
    Summarize the key steps of polynomial long division. Discuss the connection between polynomial long division and factoring. Preview the next lesson on polynomial long division with remainders.

Interactive Exercises

  • Error Analysis
    Present students with a worked-out polynomial long division problem that contains an error. Have students identify the error and correct it.
  • Partner Practice
    Have students work in pairs to solve polynomial long division problems. One student performs the steps, while the other student checks the work and provides feedback. Students alternate roles for each problem.

Discussion Questions

  • How is polynomial long division similar to and different from numerical long division?
  • What are some common mistakes to avoid when performing polynomial long division?
  • How can you check your answer after performing polynomial long division?
  • How can polynomial long division be used to solve polynomial equations?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Critical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in polynomial long division?

Correct Answer: Divide the leading terms

Question 2:

During polynomial long division, what operation do you perform after multiplying the divisor by the term you placed on top?

Correct Answer: Subtraction

Question 3:

When do you stop the process of polynomial long division?

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

Question 4:

What does it mean if the remainder is zero after performing polynomial long division?

Correct Answer: The divisor is a factor of the dividend

Question 5:

In the expression (x^3 + 2x^2 - x + 5) / (x + 1), which is the dividend?

Correct Answer: x^3 + 2x^2 - x + 5

Question 6:

What do you need to do with the signs of the second polynomial after multiplying during the long division process?

Correct Answer: Change all signs

Question 7:

What is the term for the answer you obtain after performing polynomial long division?

Correct Answer: Quotient

Question 8:

Before starting polynomial long division, it is crucial to ensure that the polynomial is in what form?

Correct Answer: Descending order

Question 9:

When performing polynomial long division, you bring down the next term from the dividend after...

Correct Answer: Subtracting

Question 10:

In the process of polynomial long division, if you encounter a missing term (e.g., no x term), what should you insert?

Correct Answer: Zero as a placeholder

Fill in the Blank Questions

Question 1:

The first step in polynomial long division is to divide the _________ terms of the dividend and divisor.

Correct Answer: leading

Question 2:

After multiplying the divisor by the term on top, you must __________ the resulting polynomial.

Correct Answer: subtract

Question 3:

The polynomial being divided is called the _________.

Correct Answer: dividend

Question 4:

The polynomial you are dividing by is called the _________.

Correct Answer: divisor

Question 5:

If the remainder is zero, the divisor is a __________ of the dividend.

Correct Answer: factor

Question 6:

The result of polynomial long division is called the _________.

Correct Answer: quotient

Question 7:

Before dividing, make sure the polynomials are arranged in __________ order of exponents.

Correct Answer: descending

Question 8:

When subtracting polynomials during long division, remember to distribute the ________ sign.

Correct Answer: negative

Question 9:

The goal of polynomial long division (in this lesson) is to obtain a remainder of _________

Correct Answer: zero

Question 10:

If a term is missing in the dividend (e.g., no x term), insert a __________ as a placeholder.

Correct Answer: zero

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

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