Mastering Factoring by Grouping

Algebra 2 Grades High School 7:03 Video
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Lesson Description

Learn how to factorize polynomials with four terms using the grouping technique. This lesson is perfect for Algebra 2 students!

Video Resource

Grouping Factoring Algebra 2

Kevinmathscience

Duration: 7:03
Watch on YouTube

Key Concepts

  • Factoring
  • Grouping
  • Common Factors

Learning Objectives

  • Students will be able to identify when factoring by grouping is an appropriate technique.
  • Students will be able to successfully factor polynomials with four terms using the grouping method.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic factoring concepts and highlighting scenarios where traditional methods don't apply (specifically polynomials with four terms). Introduce the concept of 'grouping' as a strategic approach.
  • Video Instruction (15 mins)
    Play the Kevinmathscience video on factoring by grouping. Encourage students to take notes on the steps and examples provided.
  • Guided Practice (20 mins)
    Work through example problems on the board, demonstrating the grouping process step-by-step. Emphasize the importance of checking for common factors within each group and the overall expression. Address the scenario where initial grouping doesn't work and demonstrate rearranging terms.
  • Independent Practice (15 mins)
    Assign practice problems for students to work on individually. Circulate to provide assistance and answer questions.
  • Wrap-up and Review (5 mins)
    Summarize the key steps of factoring by grouping and answer any remaining questions. Preview upcoming topics related to factoring.

Interactive Exercises

  • Group Challenge
    Divide students into small groups and provide each group with a challenging factoring by grouping problem. Have groups present their solutions and explain their process to the class.

Discussion Questions

  • When is factoring by grouping the most effective method?
  • What do you do if the initial grouping doesn't lead to a common factor between the groups?

Skills Developed

  • Algebraic Manipulation
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

Factoring by grouping is most useful when dealing with polynomials containing how many terms?

Correct Answer: 4

Question 2:

In the expression ax + ay + bx + by, what is the common factor in the first group (ax + ay)?

Correct Answer: a

Question 3:

After grouping and factoring, if the expressions in parentheses are NOT identical, what should you do?

Correct Answer: Rearrange the terms and try a different grouping

Question 4:

Which of the following is the correctly factored form of x³ + 2x² + 3x + 6?

Correct Answer: (x² + 2)(x + 3)

Question 5:

What is the first step in factoring 6xy + 8x + 15y + 20 by grouping?

Correct Answer: Group the first two terms and the last two terms

Question 6:

When factoring by grouping, which property allows you to rewrite a + b as b + a?

Correct Answer: Commutative Property

Question 7:

Factor completely: 5ab - 10a + 3b - 6

Correct Answer: (5a + 3)(b - 2)

Question 8:

What is the greatest common factor (GCF) of 4x³ + 8x²?

Correct Answer: 4x²

Question 9:

Which of the following expressions cannot be factored by grouping?

Correct Answer: x² + 2x + 3

Question 10:

If you factor by grouping and arrive at (2x + 1)(x - 3), what are the zeros of the polynomial?

Correct Answer: x = -1/2, x = 3

Fill in the Blank Questions

Question 1:

The first step in factoring by grouping is to ______ the terms into pairs.

Correct Answer: group

Question 2:

After grouping, you should factor out the ______ ______ ______ from each group.

Correct Answer: greatest common factor

Question 3:

If the binomials in the parentheses are the same, you can factor them out as a ______ ______.

Correct Answer: common factor

Question 4:

If the initial grouping doesn't work, you may need to ______ the terms.

Correct Answer: rearrange

Question 5:

Factoring by grouping is particularly useful for polynomials with ______ terms.

Correct Answer: four

Question 6:

In the expression 3ax + 6ay + 4bx + 8by, the common factor in the first group is ______.

Correct Answer: 3a

Question 7:

After factoring out common factors, the remaining expression should be a product of two ______.

Correct Answer: binomials

Question 8:

If the factored form is (x + 2)(x - 5), the solutions (or roots) of the equation are x = ______ and x = ______.

Correct Answer: -2, 5

Question 9:

When rearranging terms, it's helpful to put terms with a common ______ next to each other.

Correct Answer: factor

Question 10:

Factoring is the opposite of ______.

Correct Answer: expanding/distributing

Educational Standards

A2.A.2.1:Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies.

Teaching Materials

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