MY FAVORITE FACTORING METHOD

By Lisa Abreu

H

istory

P

urposes

E

xamples

C

onclusion

INTRODUCTION

HISTORY

B

ecause 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.

h

ttp://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 EXAMPLEST

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

F

actor 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

T

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

Fac

tor 4x2-121

4x2-

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

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

Aga

in 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