Math 10C <a class="autolink" title="Module 3 Summary" href="https://moodlehub.ca/mod/page/view.php?id=2088">Module 3 Summary</a>

Module 3: Polynomials

 

Lesson5 Summary

 

In this lesson you investigated the following questions:

  • How are perfect squares involved in the factoring of polynomials?

  • How do you select appropriate strategies for factoring polynomials?

In this lesson you discovered patterns that helped you to develop strategies for factoring special polynomials. What is common to each of these polynomials is that they both involve perfect squares. In the case of a difference of squares, you learned that

 

a2 – b2 = (a + b)(a – b)

The pattern you discovered here is that a difference of squares can be expressed as the product of the sum of the square roots and the difference of the square roots of each term in the original binomial. You also learned that this pattern is only valid in cases where the polynomial to be factored

  • is a binomial

  • has a first term that is a perfect square

  • has a second term that is a perfect square

In this lesson you also discovered patterns relating to perfect square trinomials. These trinomials are identified by the presence of two perfect squares: the x2-term and the constant. You learned that these trinomials can be factored by ordinary trinomial factoring strategies. If you can, however, identify that both the x2-term and constant are perfect squares, you can factor it as a perfect square trinomial.

You have now added many factoring strategies to your repertoire. To decide which strategy or combination of strategies to use, you must be aware of the conditions under which a strategy can be used.

Throughout the last three lessons of this module, you have learned to select strategies based on the nature of the polynomial. In all cases, you should always check each term to see if there are common factors that can be factored first. If further factoring is warranted, then you will have the added benefit of working with smaller coefficients.

Lesson 5 is the last lesson of Module 3. Remember to complete the Unit 2 Project.

You have now completed Module 3. In this module you have learned how to multiply and factor polynomials. In subsequent modules, you will continue to use factoring to achieve other objectives such as simplifying expressions and solving equations.

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