Math 10C Module 3 Lesson 4

Module 3: Polynomials

 

Lesson 4: Factoring Trinomials of the Form ax2 + bx + c

 

Focus

 

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From 1930s to the 1950s, rotor machines were state-of-the-art devices used for encrypting and decrypting secret messages. The system used a simple substitution cipher, where each letter was replaced by a different letter based on an algorithm known only to some. The most famous example is the Enigma machine used in World War II.

Times have changed. Nowadays, encryption is used for many things besides secret messages. For example, codes are used in a wide variety of commercial data-storage applications, most prominently in CDs, DVDs, and Blu-ray discs. In fact, polynomial codes are used in these applications! The properties of polynomials that allow you to add, subtract, multiply, and divide also allow a great range of coding options.

In this lesson you will continue to explore factoring strategies. In particular, you will learn how to factor trinomials of the form ax2 + bx + c, where a ≠ 1.

Outcomes

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

  • model the factoring of a trinomial in the form ax2 + bx + c, concretely or pictorially, and express the polynomial in factored form

  • express a polynomial as a product of its factors

  • factor a polynomial, and verify by multiplying factors

Lesson Questions

  • How is a multiplication array similar to a cipher?

  • How are the coefficients of a trinomial related to the coefficients of its binomial factors?

m10c_assess.jpg Lesson Assessment and Completion

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**


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