Lesson 3: Common Factors and Factoring Trinomials

Module 3: Polynomials

Lesson 3: Common Factors

Focus

both: Larrie Thomson/www.nightphotographer.com

Have you ever attended a live rock concert or any other live performance? If you have, you know that there is a lot of energy at those events. The sounds are amplified, and the visual effects on stage are spectacular.

In order for you to enjoy such a performance, many hours are dedicated to preparing for the event. Often, the stage is specially assembled for the show. Then, set pieces and music equipment are placed on the stage and many yards of cable are laid down. Fog machines and an assortment of lights are hung. Speakers are placed, and mics undergo sound checks. All of these pieces combine to produce a glamorous and visually stunning performance.

When the concert is over, the stage is disassembled and the individual pieces are packed up to be moved to the next venue.

Similarly, multiplying polynomials involves assembling smaller pieces into larger ones. In Lessons 1 and 2, for example, you learned how to multiply binomials to produce trinomials. Just as a stage can be disassembled, so too can polynomials be reduced to smaller pieces. In the remainder of this module you will learn how to break larger polynomials into smaller ones by factoring.

In this lesson you will learn strategies to factor various types of the polynomials called trinomials.

Outcomes

At the end of this lesson, you will be able to

• determine the common factors in the terms of a polynomial
• model the factoring of a trinomial of the form x2 + bx + c, concretely or pictorially, and record the process symbolically
• explain, using examples, the relationship between multiplication and the factoring of polynomials
• express a polynomial as a product of its factors
• factor a polynomial and verify by multiplying factors

Lesson Questions

• How are polynomial-factoring strategies similar to strategies used to obtain the prime factorization of a whole number?
• How can you tell if a polynomial is factored correctly?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Assess tab or by using the Quizzes link under the Activities block.

** Note – Share questions may have to be done on your own depending on your learning situation**