My Favorite Factoring Method

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My Favorite Factoring Method

  1. 1. MY FAVORITE FACTORING METHOD By Lisa Abreu
  2. 2. <ul><li>History </li></ul><ul><li>Purposes </li></ul><ul><li>Examples </li></ul><ul><li>Conclusion </li></ul>INTRODUCTION
  3. 3. HISTORY <ul><li>Because of his 1844 book called Ausdehnungslehre Hermann Grassmann could be considered the first person to formally use factoring or decomposition techiques to solve algegra problems. </li></ul><ul><li>http://darkwing.uoregon.edu/~vitulli/441.sp04/LinAlgHistory.html </li></ul>
  4. 4. PURPOSES FOR FACTORING Why is factoring important in math and life? Based on the response to a question from the blog page of www.answers.com, an author stated “…because it simplifies things, and puts them in more easily understandable terms. For most people, a long mathematical expression with squares and constants doesn't intuitively mean much. You don't get a feeling for it just by looking at it.... ” Also Carol N. Morgan-Brown, Master teacher for the New York State Department of Education stated that “factoring just creates equivalency for the sheer purpose of appeasing the eye and mind so that the brain can determine a solution.”
  5. 5. LISA EXAMPLES The following example will be factored by my favorite method called the “ Two Binomial Method / Rectangular Method… ( I created this name).” It is my favorite method because I get to create two binomials to represent the sides of a rectangle and thus get to see the origin of the trinomial. Example: 2a 2 -ab - 6b 2 Solution: (2a+3b)(a—2b) Check: 2a 2 -4ab+3ab-6b 2 Combine like terms:2a 2- ab-6b 2 2a+3b a-b2
  6. 6. LISA EXAMPLES <ul><li>The Difference of two squares for a=1; ax 2 + bx + c = y </li></ul><ul><li>Factor x 2 -64 </li></ul><ul><li>X 2 -64=x 2 -8 2 </li></ul><ul><li>=(x+8)(x-8) </li></ul><ul><li>Check :Use FOIL to multiply </li></ul><ul><li>(x+8)(x-8) </li></ul><ul><li>X 2 -8x+8x-64 </li></ul><ul><li>X 2 -64 </li></ul><ul><li>This method was chosen because it was easy to do because I know my perfect square numbers; 1,4,9,16,25 & etc. </li></ul>
  7. 7. LISA EXAMPLES <ul><li>The Difference of two squares for a 1 of ax 2 + bx + c =y </li></ul><ul><li>Factor 4x 2 -121 </li></ul><ul><li>4x 2 -121=(2x) 2 -(11) 2 </li></ul><ul><li>=(2x+11)(2x-11) </li></ul><ul><li>Again this method was chosen because it was easy for me to do. </li></ul>
  8. 8. CONCLUSION I learned the value of factoring or breaking something apart such as a polynomial that has coefficients with similar multiples such as 4x 2 + 2x = 2x(2x+1). Also, I learned the connection between binomials and linear algebra via Herman Grassmann. Specifically, he expressed that one way to get a solution or a result is to factor out a vector of data from a matrix of data. Last, this project made math a little bit more fun because I got to put my examples on the computer via Power Point 2010.
  9. 9. REFERENCES <ul><li>1)Leff. Lawrence S. Let’s review: Integrated Algebra. Hauppage, NY.: </li></ul><ul><li>Barron’s Education Series, Inc., </li></ul><ul><li>2008. </li></ul><ul><li>2)Bellman et al. New York Integrated Algebra. Boston MA: Peason Prentice Halls, 2008. </li></ul><ul><li>3)http://answers.yahoo.com/question/index?qid=20061214224232AA6SAAT </li></ul><ul><li>4)h ttp://darkwing.uoregon.edu/~vitulli/441.sp04/LinAlgHistory.html </li></ul>

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