(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

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.

Multiplying Monomials

Simplify each product

*remember this shortcut:

(       )   (       ) when there are two parentheses, you are multiplying coefficients but you add the exponents.

(       ) when there is one parentheses, you are raising the coefficient to the power outside of the parentheses and        multiplying the exponent.

when you raise a negative coefficient to a power, you will receive a positive number. For instance,

examples
=

multiply coefficients ( 2 x 4) = 8    add coefficients (3 + 2) = 5     add coefficients (y^2)

 

Find the area of the rectangle.

formula –> A = l x w

length: width:

1. Multiply coefficients

2. Add exponents of like terms (8 + 6 = 14)

3. Include the unlike term

4. Write your result:

reference: homework sheet, Breese, 1st prd

 

 

Mixed Review of Adding, Subtracting, Multiplying, and Dividing Monomials

Example of a monomial

coefficient: -14 variable: m exponent: 9

MONOMIALS RULE!

Adding/Subtracting

combine like terms when the variable and exponents are the same.

Addition answer: SUM

Subtraction answer: DIFFERENCE

Multiplying

multiply coefficients, add exponents for same variable.

Multiplication answer:  PRODUCT

Dividing

divide coefficients and subtract exponents for same variable.

Division answer: QUOTIENT

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1. =

3. =

6.=

Adding Monomials

Image via Wikipedia

A student asked this question: How do you add monomials?

The key to knowing how to add monomials is to look at the three parts of your monomial. Every monomial has three parts: the coefficient, the variable, and the exponent.

In the example below, the coefficient is 3. The coefficient is the number that appears before your variable. The variable is the letter written in your monomial. Lastly, the exponent is the number that is raised after your variable.

Here is an example of a monomial with like terms.

=you would combine like terms because the variables and exponents are the same.

Here is an example of a monomial without like terms.

 

you would not combine like terms because the exponents are different.

Note to student: refer to your worksheet Mixed review of Adding, Subtracting, Multiplying and Dividing Monomials (date March 7, 2011, under Guided Practice, box #1)