(wager) Multiplying and Dividing Monomials Benchmark Reviews

Students,

Benchmarks are quickly approaching. All of the lessons and materials that you will receive in class this week will be related to the problems that will be presented on the Benchmarks.

Let’s review…

FACTOR TRINOMIALS

The standard form for trinomials has three terms: ax^2 + bx + c, where A = 1st term, B = 2nd term, and C = 3rd term. Using the “X” method, we place our B value on the top and our C value on the bottom.

B value: sum of side numbers     C value: product of side numbers

Points to remember

• Multiplying monomials- multiply coefficients, add exponents
• Dividing monomials- divide coefficients, subtract exponents
• Exponent outside the parentheses- write term out as many times as the numbers tell you to. Parentheses mean MULTIPLY!

Check out these links below

Multiplying Powers of a Monomial

Multiplying and Dividing Monomials

Factoring Trinomials using the \”X\” method

Box Method for Factoring

Factor Using Greatest Common Factor (GCF)

Factor using the Greatest Common Factor (GCF)

If the coefficient is prime, you can still factor out variables.

ex. 5xy^3z^3 + 6x^2yz^5 – 8x^3y^2z^2   This is a prime number, however you can factor out the variables.

# of Xs: one is the lowest (x will go outside of the parentheses)

# of Ys: one is the lowest (y will go outside of the parentheses)

# of Zs: two is the lowest (z will go outside of the parentheses)

>>Once you factor this problem, you are going to receive this result:  xyz^2(5y^2z + 6xz^3 – 8x^2y)

>>We made posters today in class and you all are doing an awesome job with this topic.

FACTORING

4r^4 + 24r^5t^2

Greatest Common Factor: 4r^4

Factored form: 4r^4(1 + 6rt^2)

Multiplying positive/negative binomials with coefficients

Image by wonderferret via Flickr

What is FOIL?’

First   Outside   Inside   Last

There are two methods to use when multiply positive and negative binomials

( x + 7 )  (x – 7 )

How to Graph a Polynomial

The Smiling Man (or Monkey Face) or the Box 

1. Multiply the coefficients for all terms.

2. Combine the outer and inner terms.

TEST 3/17/11- Study tonight- Wager 3rd period

 

Test subject: Monomials, scientific and standard notation, graphing polynomial functions and adding polynomials

CHEAT SHEET- Print this if you can and study before school

Use your classwork sheet as a reference for these explanations below.

Section 1: Perform the operation on the following monomials

*REMEMBER:

(    )   (    ) = multiplication of coefficients only! Add the exponents.

___ = division of coefficients only! Subtract exponents.

If terms are alike, you do subtract/add coefficients. If they are not like terms, you do not do anything with the terms.

Section 2: Perform the operation on the following monomials with no negative or zero exponents.

*REMEMBER:

For dividing monomials-

No exponent means that the variable is raised to the first power! (1 is the exponent)

5g = 5 (g^1) or five times g to the first power

A positive exponent subtracted from a negative exponent

^-6 – (-8) = -6 +8 = -2

Section 3: Write the following numbers in scientific notation

360000000. The decimal place is at the end of the zeros. Move your decimal to the left eight times.

360000000 Rewrite this as 3.6

Everything in scientific notation is written as  x 10 ^power (times ten to the # power).

Section 4: Write the following numbers in standard notation

4. x 10^8    Since the exponent is negative, you would move your decimal place to the opposite direction. When your exponent is positive, move your decimal place to the left.

400000000 There are eight zeros because our exponent is a positive 8.

Section 5: Fill in the table for the following exponential functions and graph the parabolas.

 

 

 

 

 

 

 

 

Section 6: Combine the following polynomials where possible.

* REMEMBER:

Start with the largest exponent and combine them as the operation says.

= 

stays the same.  and are combined .   -5 + 6 = x^4 and -6x^3 stays the same.

 

GOOD LUCK   : )!

Remember, we strive to achieve 80% or more on our tests! Let’s do this.

MONOMIALS RULE!

Rules to remember for monomials

• When you multiply coefficients, you add exponents
• When you divide coefficients, you subtract exponents
• When you raise an exponent to a power, you multiply exponents