Module 3 Summary

                                                                Module 3 Summary                                                                     

Socks and shoes are sold in pairs. Without one, the other is useless. Similarly, encryption is a process that is useless without decryption. After all, what good is a secret message if nobody knows how to decode it? Encrypting and decrypting are inverse processes. Likewise, the mathematical concepts of multiplying and factoring polynomials are inverse processes. In order to reverse the effects of one, you need to apply the other.

In this module you learned how to use various strategies to combine polynomials and you also learned similar strategies for breaking them apart.

The first part of the module was analogous to encryption: you learned to build—or encode—polynomials.

At the beginning of this module, you explored binomial multiplication. The strategies you used to do this included algebra tiles, the area method, and the distributive property. You discovered that multiplying binomials is similar to multiplying a pair of two-digit numbers. You then extended the concept of binomial multiplication to polynomial multiplication. You also learned how to verify the product of a polynomial multiplication by substituting a known value into both the original expression and the product expression.

In the second half of the module, you learned to reverse polynomial multiplication by factoring. Factoring is a process that is analogous to decryption where you can express a polynomial as a product of its factors. You could use algebra tiles and the area method to determine the factors of a polynomial. You also learned, however, that there are limits to this method and that algebraic strategies were necessary to factor other more complicated expressions. Many techniques can be used for factoring trinomial expressions including the product-sum method, decomposition, and inspection. You learned to verify the factors of a polynomial by multiplying the factors to see if they corresponded to the original expression.

At the end of the module, you completed a document that helps you to review the factoring strategies. This document was the basis for a flowchart which enabled you to systematically determine the strategies to be used in the factoring of any given polynomial. As you proceeded through the lessons in this module, you had opportunities to create ciphers based on the math concepts you learned. Some of these ciphers would eventually serve as the basis for your final project.

The “Outcomes for Module 3” table summarizes the learning outcomes and corresponding learning activities in this module. Complete the table by identifying those activities that you undertook to address the corresponding outcomes.