Factoring Linear Binomials: Unlocking the Distributive Property

Algebra 1 Grades High School 3:28 Video
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Lesson Description

Learn how to factor linear binomials by identifying and extracting the greatest common factor. This lesson reinforces the distributive property in reverse and builds a foundation for more complex factoring techniques.

Video Resource

Example 1: Factor a linear binomial by taking a common factor | Algebra I | Khan Academy

Khan Academy

Duration: 3:28
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Key Concepts

  • Factoring
  • Greatest Common Factor (GCF)
  • Distributive Property (in reverse)
  • Linear Binomials

Learning Objectives

  • Students will be able to identify the greatest common factor of terms in a linear binomial.
  • Students will be able to factor out the greatest common factor from a linear binomial to rewrite it as a product of two expressions.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the distributive property. Ask students to expand expressions like 2(x + 3) to refresh their understanding. Explain that factoring is the reverse process of the distributive property.
  • Video Presentation (10 mins)
    Play the Khan Academy video 'Example 1: Factor a linear binomial by taking a common factor | Algebra I | Khan Academy.' Encourage students to take notes on the steps involved in factoring. Pause at key points to ask clarifying questions.
  • Guided Practice (15 mins)
    Work through several examples on the board, guiding students through each step. Start with simpler binomials and gradually increase the complexity. Emphasize the importance of identifying the greatest common factor correctly. Examples: 6x + 9, 10y + 25, 8a + 12
  • Independent Practice (15 mins)
    Provide students with a worksheet containing various linear binomials to factor. Encourage them to work individually and offer assistance as needed. Examples: 14x + 21, 15y + 35, 9a + 27, 20b + 30, 12x + 18.
  • Wrap-up and Assessment (5 mins)
    Review the key steps of factoring linear binomials. Collect the worksheets for assessment. Answer any remaining questions.

Interactive Exercises

  • Factor Race
    Divide the class into groups. Provide each group with a different linear binomial to factor. The first group to correctly factor their binomial wins.
  • Error Analysis
    Present students with examples of incorrectly factored binomials and ask them to identify the errors and correct them.

Discussion Questions

  • What is the distributive property, and how is it related to factoring?
  • What is the greatest common factor (GCF), and why is it important in factoring?
  • How can you check if you have factored a binomial correctly?

Skills Developed

  • Factoring
  • Problem-solving
  • Analytical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in factoring the expression 6x + 12?

Correct Answer: Find the greatest common factor

Question 2:

What is the greatest common factor of 4x and 16?

Correct Answer: 4

Question 3:

Which of the following is the factored form of 8y + 24?

Correct Answer: 8(y + 3)

Question 4:

Factoring is the reverse of which property?

Correct Answer: Distributive Property

Question 5:

What is the factored form of 5x + 10?

Correct Answer: 5(x + 2)

Question 6:

What is the greatest common factor of 9a and 18?

Correct Answer: 9

Question 7:

Which of the following is the factored form of 3x + 6?

Correct Answer: 3(x + 2)

Question 8:

What is the factored form of 7y + 14?

Correct Answer: 7(y + 2)

Question 9:

What is the greatest common factor of 12b and 36?

Correct Answer: 12

Question 10:

Which of the following is the factored form of 2x + 8?

Correct Answer: 2(x + 4)

Fill in the Blank Questions

Question 1:

The greatest common factor of 4x and 8 is ______.

Correct Answer: 4

Question 2:

Factoring is the process of rewriting an expression as a ______.

Correct Answer: product

Question 3:

The factored form of 6x + 18 is 6(x + ______).

Correct Answer: 3

Question 4:

The first step in factoring is to find the ______.

Correct Answer: GCF

Question 5:

5(x + 2) expanded is 5x + ______.

Correct Answer: 10

Question 6:

The factored form of 9y + 27 is 9(y + ______).

Correct Answer: 3

Question 7:

The greatest common factor of 10a and 20 is ______.

Correct Answer: 10

Question 8:

The factored form of 3x + 15 is 3(x + ______).

Correct Answer: 5

Question 9:

When factoring, you are ______ the distributive property.

Correct Answer: reversing

Question 10:

The factored form of 2x + 10 is 2(x + ______).

Correct Answer: 5

Educational Standards

A1.A.3.3:Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

Teaching Materials

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