Unlock Factoring Superpowers: Trinomials with Common Factors

Algebra 2 Grades High School 10:17 Video
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Lesson Description

Master the art of factoring trinomials by first identifying and extracting common factors. Learn how to simplify complex expressions and solve quadratic equations with ease.

Video Resource

Factoring Trinomials with Common Factor

Kevinmathscience

Duration: 10:17
Watch on YouTube

Key Concepts

  • Factoring Trinomials
  • Greatest Common Factor (GCF)
  • Simplifying Algebraic Expressions

Learning Objectives

  • Students will be able to identify the greatest common factor (GCF) within a trinomial expression.
  • Students will be able to factor out the GCF from a trinomial expression.
  • Students will be able to factor the resulting trinomial after extracting the GCF.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of factoring and its importance in simplifying algebraic expressions. Briefly recap factoring basic trinomials.
  • Video Presentation (15 mins)
    Play the Kevinmathscience video 'Factoring Trinomials with Common Factor'. Instruct students to take notes on the steps involved in identifying and factoring out the common factor.
  • Guided Practice (20 mins)
    Work through example problems similar to those in the video, demonstrating each step of the factoring process. Encourage student participation and answer any questions.
  • Independent Practice (15 mins)
    Assign a set of practice problems for students to work on individually. Circulate the classroom to provide assistance as needed.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts of the lesson and administer a short quiz to assess student understanding.

Interactive Exercises

  • Factor the Expression
    Provide students with a trinomial expression containing a common factor. Have them work in pairs to identify the GCF and factor the expression completely. Encourage them to verify their answers by distributing the factored expression.

Discussion Questions

  • Why is it important to look for a common factor before attempting to factor a trinomial?
  • How does factoring out a common factor simplify the factoring process?

Skills Developed

  • Algebraic Manipulation
  • Problem-Solving

Multiple Choice Questions

Question 1:

What is the first step when factoring a trinomial with a possible common factor?

Correct Answer: Check for a common factor

Question 2:

What is the greatest common factor of the expression 6x² + 12x - 18?

Correct Answer: 6

Question 3:

After factoring out the GCF, what type of expression are you typically left with?

Correct Answer: Trinomial

Question 4:

Which of the following is the correct factorization of 3x² + 15x - 36?

Correct Answer: 3(x² + 5x - 12)

Question 5:

What combination of factors of -24 would add up to -5?

Correct Answer: -8 and 3

Question 6:

What is the next step after you identify that the factors of your constant are 2 and 15 if you are trying to get the 'b' value of 13?

Correct Answer: 15-2

Question 7:

What is a trinomial?

Correct Answer: A polynomial with three terms

Question 8:

In what order should you pull out factors of an expression?

Correct Answer: Factors of numbers then variables

Question 9:

What is -4 - 9?

Correct Answer: -13

Question 10:

What two numbers multiply to 50 but also can subtract to give you -5?

Correct Answer: 5 * -10

Fill in the Blank Questions

Question 1:

The first step in factoring trinomials with common factors is to identify the __________.

Correct Answer: GCF

Question 2:

After factoring out the GCF, you should be left with a simpler __________ to factor.

Correct Answer: trinomial

Question 3:

Factoring is the opposite of __________.

Correct Answer: distribution

Question 4:

Always verify your factored expression by __________ it back out to the orginal expression.

Correct Answer: multiplying

Question 5:

The process of finding common factors applies to __________ types of polynomials.

Correct Answer: all

Question 6:

If there is not a constant GCF, look to see if a common __________ can be pulled from each term.

Correct Answer: variable

Question 7:

If all the signs of the trinomial are negative, start by factoring out a __________.

Correct Answer: negative

Question 8:

Factoring a trinomial involves finding two __________ whose product equals the trinomial.

Correct Answer: binomials

Question 9:

The first step in solving any expression is to always check for a _________ ___________.

Correct Answer: common factor

Question 10:

4x^2 + 8x + 12 has the common factor of __________.

Correct Answer: 4

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. A2.A.2.2:Add, subtract, multiply, divide, and simplify polynomial expressions.

Teaching Materials

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