Period 5

Algebra II

Mr. Young

3^rd Quarter Web Page

Email: R_Kreymborg@fayar.net

üüPOINTS OF INTERESTüü

F Combining Like Terms

F Multiplying Polynomials

F Factoring

vØèCOMBINING LIKE TERMSç×v

If the polynomial has the same variables raised to the same powers, the terms are called LIKE TERMS.

Example: 5a+2-8a can be simplified to –3a+2

You cannot combine letters with numbers with just plain numbers! Anything with an exponent can only be joined with other letters or numbers with exponents.

l^›Multiplying Polynomials^›l

This is where F.O.I.L comes in. When you are multiplying two polynomials; you must do your firsts, outsides, insides, and last numbers in both sets of parentheses or F.O.I.L.

Example: (x+4)(x-4)= x^2-16

(x-2)(x+2)= x^2-4

(4x-2)(4x+2)= 16x^2-4

°fªFactoringfª°

This is the reverse of multiplication. You must look for the GREATEST COMMON FACTOR. ²You must beware of signs when your third term is proceeded by a minus sign.²

[image]

“GRAPH“

There is only one line here on the graph because the two equations I chose to enter into y= caused only one line to show up.

èThe first equation I wrote was

(x^3-27).

èThe second equation I wrote was

(x-3)(x^2+3x+9)

The second equation is the factored form of the first equation therefore, they created the same line when they were graphed, giving the appearance of one line.

2.http://www.northern.wvnet.edu/~srychlicki/sr1/slide1.htm

3.http://math.usask.ca/readin/factor.html

4.http://www.thinkquest.org/library/lib/site_sum_outside.html?tname=20991&url=20991/alg2/polyf.html

5.http://www.sosmath.com/algebra/factor/fac06/fac06.html

6.http://www.math.csusb.edu/math110/src/poly/factandgraph.html

7.http://www.visi.com/~dethier/activities/mac-graph/mac-graph-polyn.htm

fI chose to do my web page over this topic, because factoring was a fun section that we spent a lot of time on in our Algebra II class this year. Factoring starts out as a very simple process, but you have lots of little things that weigh into the completion of the process. You can solve the problems a number of different ways for some variety. Problems can be solved with just plain factoring by hand, the graphing calculator, or by TI Interactive.

Excerpts of History Taken From Various Web Sites Concerning Polynomials

Chebotaryov worked on the algebra of polynomials, in particular examining the distribution of the zeros. He also studied Galois theory writing a two- volume textbook Basic Galois Theory (1934, 1937) and being the moving force in having the first translation of Galois's works into Russian in 1936. Other important work was on Lie groups, and on this topic he wrote the first Russian text Theory of Lie Groups (1940), He also did important work on the inverse Galois problem and the theory of resolvants.

After further papers on subgroups of infinite abelian groups and normal numbers he wrote a series of eight papers on Arithmetic on curves of genus 1. Then in 1959 he published another book, An introduction to the geometry of numbers. Among work undertaken after this was work on the representation of rational functions as sums of squares, integral points on certain elliptic curves, Kummer sums, and on factorising polynomials in several variables.

&I&THE END&I&