Mastering Factoring Trinomials: Splitting the Middle Term

Algebra 2 Grades High School 1:31 Video
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Lesson Description

This lesson provides a step-by-step guide to factoring trinomials of the form ax² + bx + c where a ≠ 1, using the splitting the middle term and factoring by grouping method.

Video Resource

Factoring Trinomials a≠1 Using Splitting Middle Term and Factoring by Grouping Method

Mario's Math Tutoring

Duration: 1:31
Watch on YouTube

Key Concepts

  • Factoring trinomials with a leading coefficient
  • Splitting the middle term
  • Factoring by grouping

Learning Objectives

  • Students will be able to identify trinomials with a leading coefficient.
  • Students will be able to split the middle term of a trinomial into two terms that satisfy specific multiplication and addition conditions.
  • Students will be able to factor trinomials by grouping after splitting the middle term.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic factoring concepts and the standard form of a trinomial (ax² + bx + c). Briefly explain why factoring is an important skill in algebra. Introduce the challenge of factoring trinomials where 'a' is not equal to 1.
  • Video Viewing and Note-Taking (10 mins)
    Play the video 'Factoring Trinomials a≠1 Using Splitting Middle Term and Factoring by Grouping Method' from Mario's Math Tutoring. Instruct students to take notes on the steps involved in the splitting the middle term method.
  • Example 1 Walkthrough (10 mins)
    Work through the first example (2x² + 5x + 2) from the video on the board, pausing at each step to explain the reasoning behind it. Emphasize how to find the two numbers that multiply to (a*c) and add up to 'b'. Show how these numbers are used to split the middle term. Walk through the factoring by grouping steps clearly.
  • Example 2 & 3 Guided Practice (15 mins)
    Present the second example (3x² - 26x + 16). Guide students through the initial steps (finding the two numbers to split the middle term) as a class. Then, have them complete the factoring by grouping on their own or in pairs. Review the solution. Repeat with Example 3 (10x² + 11x - 6).
  • Independent Practice (15 mins)
    Provide students with a set of trinomials (a ≠ 1) to factor using the splitting the middle term and factoring by grouping method. Circulate the room to provide assistance as needed.
  • Wrap-up and Q&A (5 mins)
    Summarize the key steps of the splitting the middle term method. Answer any remaining questions students may have. Preview the next lesson on other factoring techniques.

Interactive Exercises

  • Error Analysis
    Provide students with trinomial factoring problems that have been solved incorrectly. Have them identify the error and correct the solution.
  • Group Factoring Race
    Divide students into small groups. Give each group a different trinomial to factor. The first group to correctly factor the trinomial wins.

Discussion Questions

  • Why is it important to find the correct two numbers to split the middle term?
  • How does factoring by grouping work?
  • Can all trinomials be factored using this method? Why or why not?

Skills Developed

  • Factoring polynomials
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

What is the first step in factoring a trinomial by splitting the middle term?

Correct Answer: Find two numbers that multiply to ac and add to b

Question 2:

To factor 6x² + 13x + 5, what two numbers would you use to split the middle term?

Correct Answer: 10 and 3

Question 3:

After splitting the middle term, what method is used to further factor the expression?

Correct Answer: Factoring by Grouping

Question 4:

What is the factored form of 2x² + 7x + 3?

Correct Answer: (2x + 1)(x + 3)

Question 5:

When factoring 4x² - 8x + 3, the two numbers used to split the middle term are:

Correct Answer: -6 and -2

Question 6:

Which of the following expressions cannot be factored using the splitting the middle term method?

Correct Answer: x² + x + 1

Question 7:

In the trinomial ax² + bx + c, 'a' represents the:

Correct Answer: Coefficient of the x² term

Question 8:

Factoring by grouping relies on identifying a common _______ between two groups of terms.

Correct Answer: Factor

Question 9:

What is the factored form of 5x² - 13x + 6?

Correct Answer: (5x - 3)(x - 2)

Question 10:

The greatest common factor (GCF) should be factored out ________ splitting the middle term, if possible.

Correct Answer: Before

Fill in the Blank Questions

Question 1:

When factoring a trinomial of the form ax² + bx + c, you need to find two numbers that multiply to ______ and add to ______.

Correct Answer: ac

Question 2:

The method of splitting the middle term is also known as factoring by ______.

Correct Answer: grouping

Question 3:

In the expression 3x² + 7x + 2, the 'a' value is ______.

Correct Answer: 3

Question 4:

Before splitting the middle term, always check for a ______ to simplify the expression.

Correct Answer: GCF

Question 5:

When factoring 4x² + 12x + 5, the two numbers that split the middle term are 10 and ______.

Correct Answer: 2

Question 6:

The factored form of x² - 5x + 6 is (x - 2)(______)

Correct Answer: x - 3

Question 7:

Factoring is the reverse process of ______.

Correct Answer: multiplying

Question 8:

In factoring by grouping, you create two groups of ______ terms each.

Correct Answer: two

Question 9:

To split the middle term in 2x² - 5x - 3, you would rewrite -5x as -6x ______ x.

Correct Answer: +

Question 10:

The final step in factoring by grouping is to factor out the common ______.

Correct Answer: binomial

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.

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