Mastering Factoring: Tackling Trinomials with Leading Coefficients Greater Than 1

Algebra 2 Grades High School 16:07 Video
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Lesson Description

This lesson provides a comprehensive guide to factoring trinomials where the leading coefficient is greater than 1, a crucial skill in Algebra 2. Learn a systematic approach to break down complex trinomials and simplify them into factored form.

Video Resource

Factoring Trinomials with a Greater Than 1

Kevinmathscience

Duration: 16:07
Watch on YouTube

Key Concepts

  • Trinomials
  • Factoring
  • Leading Coefficient
  • Factors

Learning Objectives

  • Students will be able to identify trinomials with a leading coefficient greater than 1.
  • Students will be able to apply a systematic method to factor trinomials with a leading coefficient greater than 1.
  • Students will be able to verify factored expressions by multiplying them back to the original trinomial.
  • Students will be able to recognize when a trinomial cannot be factored.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic factoring techniques and defining 'leading coefficient'. Briefly discuss why factoring trinomials with a leading coefficient of 1 is simpler. Introduce the challenge of factoring when the leading coefficient is greater than 1, highlighting that common factor extraction should be attempted first.
  • Video Viewing (15 mins)
    Play the Kevinmathscience video 'Factoring Trinomials with a Greater Than 1'. Encourage students to take notes on the method presented in the video. Emphasize the trial-and-error approach of finding the correct combinations of factors.
  • Guided Practice (20 mins)
    Work through several example problems on the board, mirroring the method shown in the video. Involve students in each step, asking for their input on possible factors and combinations. Emphasize the importance of checking the factored expression by multiplying it out using the FOIL method or the distributive property.
  • Independent Practice (15 mins)
    Assign a set of practice problems for students to work on individually. Circulate the classroom to provide assistance and answer questions. Encourage students to work together and discuss their approaches.
  • Wrap-up and Assessment (5 mins)
    Review the key steps of the factoring method. Address any remaining questions or misconceptions. Administer a short quiz to assess student understanding.

Interactive Exercises

  • Factor Combination Game
    Divide the class into groups. Provide each group with a trinomial (e.g., 2x^2 + 7x + 3). The first group to correctly factor the trinomial and verify their answer wins a small prize.

Discussion Questions

  • What makes factoring trinomials with a leading coefficient greater than 1 more challenging than when the leading coefficient is 1?
  • Can you explain in your own words the steps involved in factoring a trinomial with a leading coefficient greater than 1?
  • Why is it important to check your factored expression by multiplying it out?
  • Are there any situations where a trinomial with a leading coefficient greater than 1 cannot be factored?

Skills Developed

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

Multiple Choice Questions

Question 1:

Which of the following is a trinomial with a leading coefficient greater than 1?

Correct Answer: 3x^2 - 2x + 1

Question 2:

What is the first step you should attempt when factoring a trinomial with a leading coefficient greater than 1?

Correct Answer: Check for a greatest common factor (GCF)

Question 3:

Which factored form is equivalent to 2x^2 + 5x + 2?

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

Question 4:

What method is recommended to check if your factored trinomial is correct?

Correct Answer: FOIL method (First, Outer, Inner, Last)

Question 5:

What are the factors of the leading coefficient in the trinomial 3x^2 + 10x + 8?

Correct Answer: 1 and 3

Question 6:

When factoring 5x^2 - 13x + 6, which pair of factors of 6 might be useful in finding the correct combination?

Correct Answer: -2 and -3

Question 7:

The factored form of 4x^2 - 4x - 3 is:

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

Question 8:

If you can't find integer factors that work, what does that suggest about the trinomial?

Correct Answer: It's prime (cannot be factored with integers)

Question 9:

Which step involves distributing the terms in each binomial to verify your factored form?

Correct Answer: Expanding

Question 10:

In factoring 6x^2+ 11x - 10, which of the following factor pairs of -10 could potentially lead to the correct middle term coefficient?

Correct Answer: -2 and 5

Fill in the Blank Questions

Question 1:

A polynomial with three terms is called a __________.

Correct Answer: trinomial

Question 2:

The number in front of the x^2 term in a trinomial is called the __________ __________.

Correct Answer: leading coefficient

Question 3:

Before factoring, you should always check for a __________ __________ __________ that can be factored out.

Correct Answer: greatest common factor

Question 4:

When factoring, you are trying to rewrite the trinomial as a product of two __________.

Correct Answer: binomials

Question 5:

The __________ method is a useful way to expand the product of two binomials.

Correct Answer: FOIL

Question 6:

If a trinomial cannot be factored using integer coefficients, it is called __________.

Correct Answer: prime

Question 7:

Factoring is the opposite of __________.

Correct Answer: expanding

Question 8:

The trial-and-error method involves testing different __________ of the leading coefficient and constant term.

Correct Answer: factors

Question 9:

In the expression 5x^2 + 3x - 2, the constant term is __________.

Correct Answer: -2

Question 10:

After factoring, always __________ your solution back into the original expression to ensure correctness.

Correct Answer: multiply

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:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

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