Key Terms in Chapter 7

Here are some of the key terms that are used throughout chapter 7, the GCF is one of them but that has already been posted!

Prime polynomial: a polynomial that can't be factored with integer coefficients

Standard form of a quadratic equation: An equation that can be written in the form
ax^2+bx+c=0, where a can't be equal to 0.

Factoring Polynomials

If you are confused how to factor, this website explains step by step how to factor polynomials

http://www.jamesbrennan.org/algebra/polynomials/factoring_polynomials.htm

Greatest Common Factor (GCF)

Greatest Common Factor (GCF)
- The largest value integer that can go into each term of an expression or set of numbers

Remember

When subtracting a polynomial remember to flip all of the signs in the second expression.

Studying

Another good way to study for the test is to do the chapter test.  You can also do the problems in the yellow boxes throughout the chapter.

Good luck everyone!

Multiplying Polynomials!

Here is a link to help with any issues with multiplying polynomials

http://www.youtube.com/watch?v=fGThIRpWEE4

Dividing Polynomials Link

Here is a link to a website that shows you step by step how to divide polynomials by long division. This one does it a little differently than others we have seen, it doesn't show a video, it just shows it written out. I found it really helpful!

http://www.sosmath.com/algebra/factor/fac01/fac01.html

Multiplying Polynomials - Methods

3 Methods-

Multiplying vertically:
You put one of the polynomials above the other and multiply one term at a time. You multiply the same as when you are multiplying: 47 times 36.

Horizontal Method:
You start out with this method by setting up the two polynomials, and then you multiple the first time in the first polynomial by the first one in the second polynomial. Then you multiply the first term in the first polynomial by the second term in the second polynomial. It is distributing. Then you do that for all of the terms.

Foil:
This method only works when multiplying binomials.
You start out the same way as the horizontal method, and then once you have multiplied all of the terms together, you combine like terms.

Adding & Subtracting Functions For Test

Remember this is how you add and subtract functions

f(x) + g(x) = ( f + g ) (x)
f(x) - g(x) = ( f - g ) (x)

EXAMPLE :

f(x) = 5x - 10
g(x) = 3x + 7

(5x- 10 + 3x + 7) =  8x - 3
(5x- 10 - 3x + 7 ) = -8x - 3

Polynomial Long Division

I had trouble the most with polynomial long division and purple math definitely helps you with every step. Long division requires a lot of steps . Check out the first  page and problem. It helped me a lot.

http://www.purplemath.com/modules/polydiv2.htm

Rules of Exponents help

If the bases of the exponential expressions that are multiplied are the same, then you can combine them into one expression by adding the exponents.


http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsRules.xml

#72 from the Chapter Review

Can anyone help me figure out #72 from the Chapter Review Problems?

72. (2k-1) - (3k^2-2k+6)

Long division

I know that people had some problems with long division so I found this website and even though this takes a little while to read its worth it, it goes through all kinds of examples and it goes through a lot of methods.
Page 2 and 3 are the best.
http://www.purplemath.com/modules/polydiv3.htm

Adding and Subtracting Functions

When I was making my study guide for 6.3 I found that I was still kind of confused with adding and subtracting functions so I looked around the internet and found this website: http://www.mathwarehouse.com/algebra/relation/adding-subtracting-function.php
it has all kinds of practice problems and explains it really well.
Brigid

Danielle, Scientific Notation

There are several problems in the Chapter Review having to do with Scientific Notation, if you are still having trouble purple math explains it very well.

http://www.purplemath.com/modules/exponent3.htm

6.1 Study Guide!

6.1: Integer Exponents and Scientific Notation

Product Rule for Exponents:
If m and n are natural numbers and a is any real number, then
am*an=am+n
In words. when multiplying powers of like bases, keep the same base and add the exponents.

Zero Exponent:
If a is any nonzero real number, then
a0=1

Negative Exponent:
For any natural number n and any nonzero real number a,
a-n=1/an

Quotient Rule for Exponents:
If a is any nonzero real number and m and n are integers, then
am/an= am-n

Power Rules for Exponents:
If a and b are real umbers and m and n are integers, then
(a) (am)^n= amn
(b) (ab)^m=ambm
( c) (a/b)^m=am/bm when b is not equal to zero


Scientific Notation:
A number is written in scientific notation when it is express in the form
a*10n

Converting to Scientific Notation:
Step 1. Position the decimal point. Place a caret ^, to the right of the first nonzero digit, where the decimal point will be placed.

Step 2. Determine the numeral for the exponent. Count the number of Digits from the decimal point to the caret. This number gives the absolute value of the exponent on 10.

Step 3. Determine the sign for the exponent. Decide whether multiplying by 10n should make the result of Step 1 larger or smaller. The exponent should be positive to make the result larger, it should be negative to make the result smaller.

Converting From Scientific Notation:
Multiplying a number by a positive power of 10 makes the number larger, so move the decimal point to the right n places if n is positive in 10n.
Multiplying by a negative power of 10 makes a number smaller, so more the deimal point to the left n places if n is negative.
If n is 0, leave the decimal point where it is.

6.3 Terms

Indentity Function: The simplest polynomial function is the idenity function defined by f(x)=x
Squaring Function: The polynomial function defined by f(x)=x^2 is called the squaring function.
Cubing Function: The polynomial function defined by f(x)=x^3 is called the cubic function.

Quiz Yourself!

Page 359- Quiz

1. A Polynomial is an algebraic expression made up of

a. a term or a finite product of terms with positive numbers

b. The sum of two or more terms with whole number coefficients and exponents

c. The product of two or more terms

d. a term or a finite sum of terms with real coefficients and whole numbers.

Multiplying Polynomials Examples

(x + 2y)(3x – 4y + 5)

(x + 2y)(3x – 4y + 5)

= 3x2 – 4xy + 5x + 6xy – 8y2 + 10y Add 6xy and 4xy because they are like terms

= 3x2 + 2xy + 5x – 8y2 + 10y



(a+b) (c+d)=ac+ad+bc+bd



(2x+3) (xz-a)= 2x^2z-2xa+3xz-3a

Reminders about Multiplying Polynomials

http://www.mathsisfun.com/algebra/polynomials-multiplying.html

Includes the videos, too.

Review for Chapter 6 Test!

Even though the test isn't until next week, it is still good to start reviewing early!
So far in this chapter we have learned about:
- Integer exponents and Scientific notation
-Adding and Subtracting polynomials
-Polynomial functions
-Multiplying Polynomials
- Dividing Polynomials
On page 360 in our books, there is a review page that has a summary of all of the things we have learned in chapter 6 it is a really helpful page to review! Also doing the chapter test and chapter review problems are also very helpful! Another thing you could do is to look at your notes from this chapter on google docs!

SRIBEY POST?!

dividing polynomials

When dividing a polynomial by a monomial you break the problem up.
ex: 9^2+3/3
9^3/3+3/3

for more on how to do this you should check out this website:

http://www.mathsisfun.com/algebra/polynomials-dividing.html

Dividing Polynomials

5x^2 +25/ 3x+2

1. Factor

2. LONG DIVISION !


2x^2+2x/x+1 this is a binomial divided by a binomial

2x is common here..always look for common factors

factor numerator then cancel out like terms

Polynomial long division

Divide numerator by denominator

1. denominator goes first
2. then a ")"
3. then a numerator with a line above
4. get them in correct order

Adding polynomials when given the value of x

(f+g)(5)
f(x)=4x^2+8x-3
g(x)=-5x^2+4x-9
Plug in 5 everywhere for x and follow the order of operations
4(25)+40-3+-5(25)+20-9

subtracting functions

when subtracting functions such as (f-g)(x) (4x^2+8x-7)-(-5x^2+4x-9) you distribute the negative.
the subtraction sign is basically -1.

f(x) info

f(x)---->y+x^2+3x-4

(f+g)x Polynomial f + polynomial g

f(3) Polynomial f with an input of 3 instead of x, you can input anything you want.
3^2+3(3)-4

9+9-4

=14

p+m(7)=p(7)+m(7)

Dividing Polynomials

To divide a polynomial by a monomial,divide each term in the polynomial by the monomial, and then write each fraction in lowest terms

examples here: http://www.purplemath.com/modules/polydiv.htm

Vertical Multiplying Polynomials!

http://www.purplemath.com/modules/polymult.htm

First step: Simplify (x + 3)(x + 2)

Second Step: top terms = (x + 3)

Second terms= (x + 2)

like a regular multiplication problem, you set up the equation like this:

Third step: multiply the 2 and the 3 and then the 2 and the x.

then the x and 3 and the x and x.

Step 4: you add your answers and end up with: x² + 5x + 6!

Multiplying Polynomials - YourTeacher.com - Algebra Help

F.O.I.L.

foil method is used to multiply two binomials.

F = first
O= outside
I = inner
L = last

adding polynomials extra help on this website

http://www.mathsisfun.com/algebra/polynomials-adding-subtracting.html

Jared Scribe post 6.2 adding and subtracting polynomials

A polynomial is a term or finite sum of the terms in which all variables have a whole number exponents and no variables appear in denominators or under radicals.
Here are more examples of polynomials: 3x-5, 4m^3-5m^2p+8, and -5t^2s^3.  REMEMBER, all monomials, binomials, and trinomials are polynomials.
To subtract two polynomials, add the first polynomial and the negative of the second polynomial.  

(-6m^2 -8m + 5) - (-5m^2 + 7m -8), change every sign in the second polynomial to add -6m^2 -8m +5 +5m^2 -7m + 8= -6m^2=5m^2-8m-7m+5+8 = -m^2-15 is the answer!!

To add polynomials combine like terms

(3a^5 - 9a^3 + 4a^2) + (-8^5 + 8a^3 + 2)
3a^5 - 8a^5 - 9a^3 + 8a^3 + 4a^2 + 2 = -5a^2 - a^3 + 4a^2 + 2

The next scribe will be done by Cole!

adding polynomials

When adding polynomials you can only add numbers and variables with the same exponents.

For Example: (3a^5-9a^3+4a^2) + (-8a^5+8a^3+2)
3a^5+(-8a^5)-9a^3+8a^3+4a^3+4a^2+2
= -5a^5-a^3+4a^2+2

Polynomial notes

a polynomial is a number and variable combination

monomial-1term
2, -6,4x, 9b^2, -3t^40

binomial-two terms
v+2, -6+2f, 3+4x, 2a^2-9
trimomal-3 terms
3y^2 +y+2, c+6-c^3

more than 3 terms polynomial

the degree of a polynomial is determined by the polynomials largest exponent

3v^4 + 4v^5+-3v+5 degree 5

7+4j^2 - 6j degree 2

basketball games

I was at the pace game and the Landmark Christian game.

Ike Scribe Post! OMG! POLYNOMIALS!!!

Today in class we covered the amazingly interesting topic of POLYNOMIAL BASICS! YAY!
And here is a review of the material:

Polynomial: "a number and variable combination consisting of one or more terms."

MONOMIAL: one term: 2X, 4, 950C
BINOMIAL: two terms: V+7, 234C-44
TRINOMIAL: three terms, 439+V+449430X

DEGREE- "Determined by the largest exponent in the Polynomial!"

So, " 3x^6 + X + 32Y^4 " would have the degree of six, because that is the largest exponent.
Simple!
However, the above polynomial [expression] is not written in the correct form. The correct form
would be to write each piece of the polynomial in greatest to smallest order, using their exponents as what to count. So, the above statement should be correctly written
" 3X^6 + 32Y^4 + X ".

{Naming polynomials BASED ON THEIR DEGREE!}
If the degree is ...
ZERO-"constant"
ONE-"linear"
TWO-"quadratic"
THREE-"cubic"
FOUR-"quartic"
FIVE-"quintic"
And if your polynomial has an expression greater than five, you simply refer to it as "polynomial of ____ degree."

The next scribe post can be... Jared. :)

6.2 Terms

polynomials=A number and a variable combination consisting of one or more terms.
monomial= having one term
binomial=having 2 terms
trinomial= having 3 terms
Degree= Degree of a polynomial is determined by the polynomials largest exponent.
Order= Polynomials like to be in degree order. The variable with the highest exponent should be first.
Naming polynomials based on degree
Degree of 0= Constant
Degree of 1= Linear
Degree of 2= Quadratic
Degree of 3= Cubic
Degree of 4= Quartic
Degree of 5= Quintic
Degree greater than 5=...of degree...

???? weird symbols

How can we get these symbols to stop showing up on the blog cause I cant read what people are saying.

Daily Quiz #1 Properties of Exponents

6.1: Scientific Notation

Using a Calculator to Compute Scientific Notation

To enter numbers in scientific notation, you can use the EE or EXP key on a scientific calculator.

Ex. 1,920,000 x .oo15/ .oooo32 x 45,000

On calculator:

1.92 EE 6 x 1.5 EE 3 +/- ? (3.2 EE 5 +/- x 4.5 EE 4)=

The EXP key is used in exactly the same way. Notice that the negative exponent -3 is entered by pressing 3, then +/-.

6.1 Scientific Notation

Converting to Scientific Notation:

Step 1: Position the decimal point. Place a caret, ^, to the right of the first nonzero digit, where the decimal point will be placed.

Step 2: Determine the numeral for the exponent. Count the number of digits from the decimal point to the caret. This number gives the absolute value of the exponent on 10.

Step 3: Determine the sign for the exponent. Decide whether multiplying by 10^n should make a result of step 1 larger or smaller. The exponent should be positive to make the result larger; it should be negative to make the result smaller.

EXAMPLE:

820,000→8.20,000→8.2 x 10^5

6.1 Integer Exponents and Scientific Notation

Product Rule for Exponents
If m and n are natural numbers and a is any real number then a^m*a^n=a^m+n
When multiplying powers of like bases keep the same base and add the exponents.

If a is any nonzero real number then a^0=1

Negative exponent
For any narural number n and any nonzero real number a a^-n=1/a^n

Special Rules for Negative Exponents
If a is does not equal 0 and be does not equal 0 then 1/a^n=a^n and a^-n/b^-m=b^m/a^n


If a is any nonzero real number and m and n are integers, then a^m/a^n=a^m-n

It's Your Time to Shine!

Start your second term off right!  Know the expectations and have a plan for success!