1. By Kyle Muldrow

2. Overview  General Description  Review of Flowcharts and Flowchart Symbols  The Factoring Flowchart  Greatest Common Factor  Factoring Polynomials with two terms  Factoring Polynomials with four terms  Factoring Polynomials with three terms  Definition of “The Blanks Method”  Definition of “The Modified Blanks Method”  Interactive Session

3. General Description  In Beginning Algebra, Intermediate Algebra, and College Algebra courses, one topic that is covered is factoring polynomials with two, three, or four terms.  Many factoring techniques are discussed.  Factoring by grouping  Perfect Square  Difference of Squares  Sum/Difference of Cubes

4. General Description (cont’d)  However, students don’t only need to know the techniques – they must also know when to use each technique.  Textbooks might have suggestions, but they are usually limited to a list that references sections of the book.  “The Factoring Flowchart” combines elements of a programming flowchart along with new terminology to give students and teachers a diagram to follow to find the right fact0ring technique.

5. Review of Flowcharts  A flowchart is “a diagram that graphically depicts steps that take place in a computer program.” [1]  Commonly used symbols are the terminal symbol (oval), the processing symbol (rectangle), and the decision symbol (diamond). 1. Tony Gaddis, Programming Logic and Design, 2 nd Edition, pgs. 32, Pearson Education, Inc. (publishing as Addison-Wesley), New York City, NY, ISBN 978-0-13-607333-2 (2010)

6. Flowchart Symbols  Terminal Symbol  Indicates the Start and End of a program [1]  Processing Symbol  Indicates processing (math calculations) done in a program [1]  Decision Symbol  Indicates a condition that must be tested [1]  All symbols are connected by arrows to represent the “flow” of the program. [1] 1. Tony Gaddis, Programming Logic and Design, 2 nd Edition, pgs. 32, 126-127, Pearson Education, Inc. (publishing as Addison-Wesley), New York City, NY, ISBN 978-0-13-607333-2 (2010)

8. Greatest Common Factor (GCF)

9. Factoring Polynomials with two terms 2. Margaret L. Lial, John Hornsby, and Terry McGinnis, Beginning Algebra, 12 th Edition, pgs. 423 and 426, Pearson Education, Inc., New York City, NY, ISBN 978-0-321-96933-0 (2012)

10. Difference of Squares and Sum of Cubes

11. Difference of Cubes

12. Factoring polynomials with four terms (Grouping)

13. Factoring polynomials with three terms 2. Margaret L. Lial, John Hornsby, and Terry McGinnis, Beginning Algebra, 12 th Edition, pgs. 423 and 426, Pearson Education, Inc., New York City, NY, ISBN 978-0-321-96933-0 (2012)

14. Perfect Square

15. The “Blanks” Method

16. The “Blanks” Method (cont’d)

18. The “Modified Blanks” Method  The “Modified Blanks” Method is a factoring technique that can be used to factor a polynomial that meets all of the following conditions:  The polynomial has three terms  The polynomial does not have 1 as its leading coefficient  The polynomial is not a perfect square  This method can still be used on a perfect square rather than the perfect square formula seen earlier.

19. “Modified Blanks” (cont’d)

21. Summary  The Factoring Flowchart can be used to determine the proper factoring technique to use when factoring polynomials with two, three, or four terms.  The first step is to check if a Greatest Common Factor can be factored out of all the terms.  Polynomials with two terms can be factored using Difference of Squares, Sum of Cubes, and Difference of Cubes.  Polynomials with three terms can be factored by using Perfect Square, The “Blanks” Method, and The “Modified Blanks” method.  Polynomials with four terms can be factored by using Factoring by Grouping.

22. References 1. Tony Gaddis, Programming Logic and Design, 2 nd Edition, pgs. 32, 126-127, Pearson Education, Inc. (publishing as Addison- Wesley), New York City, NY, ISBN 978-0-13- 607333-2 (2010) 2. Margaret L. Lial, John Hornsby, and Terry McGinnis, Beginning Algebra, 12 th Edition, pgs. 423 and 426, Pearson Education, Inc., New York City, NY, ISBN 978-0-321-96933-0 (2012)