MY FAVORITE FACTORING METHOD

By Lisa Abreu

History

Purposes

Examples

Conclusion

INTRODUCTION

HISTORY

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.

http://darkwing.uoregon.edu/~vitulli/441.sp04/

LinAlgHistory.html

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.”

LISA EXAMPLESThe 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: 2a2 -ab - 6b2

Solution: (2a+3b)(a—2b)

Check: 2a2-4ab+3ab-6b2

Combine like terms:2a2-ab-6b22a+3b

a-b2

LISA EXAMPLES

The Difference of two squares for a=1; ax2 + bx + c = y

Factor x2-64

X2-64=x2-82

=(x+8)(x-8)

Check :Use FOIL to multiply

(x+8)(x-8)

X2-8x+8x-64

X2-64

This method was chosen because it was easy to do because I know my

perfect square numbers; 1,4,9,16,25 & etc.

LISA EXAMPLES

The Difference of two squares for a 1 of ax2 + bx +

c =y

Factor 4x2-121

4x2-121=(2x)2-(11)2

=(2x+11)(2x-11)

Again this method was chosen because it was easy for

me to do.

CONCLUSION

I learned the value of factoring or breaking something apart such as a

polynomial that has coefficients with similar multiples such as 4x2 + 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.

REFERENCES

1)Leff. Lawrence S. Let’s review:

Integrated Algebra. Hauppage, NY.:

Barron’s Education Series, Inc.,

2008.

2)Bellman et al. New York Integrated

Algebra. Boston MA: Peason Prentice

Halls, 2008.

3)http://answers.yahoo.com/question/

index?qid=20061214224232AA6SAAT

4)http://darkwing.uoregon.edu/

~vitulli/441.sp04/LinAlgHistory.html