3. HISTORY
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.
ttp://darkwing.uoregon.edu/~vitulli/441.sp04/LinAlgHistory.html
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. 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: 2a2
-ab - 6b2
Solution: (2a+3b)(a—2b)
Check: 2a2
-4ab+3ab-6b2
Combine like terms:2a2-
ab-6b2
2a+3b
a-b2
6. LISA EXAMPLES
he Difference of two squares for a=1; ax2
+ bx + c = y
actor x2
-64
2
-64=x2
-82
(x+8)(x-8)
heck :Use FOIL to multiply
x+8)(x-8)
7. LISA EXAMPLES
he Difference of two squares for a 1 of ax2
+ bx + c =y
actor 4x2
-121
x2
-121=(2x)2
-(11)2
=(2x+11)(2x-11)
8. 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.
9. 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.s
p04/LinAlgHistory.html
10. 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.s
p04/LinAlgHistory.html
