Mod. 7 Review

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07.10 Module Seven Review and Practice Test
In this module, you learned about polynomials and how to perform various operations on them. This is your opportunity to review all of the concepts from this module to prepare for your Discussion Based Assessment and Module 7 Test. Introduction to Polynomials: Lesson 07.01

Polynomials are a specific type of mathematical expression that have: * one or more terms
* variables with only positive whole number exponents
* no variables in the denominators of each term
Polynomials are classified based on the number of terms and the degree. * -------------------------------------------------
Degree
* A Monomial is a polynomial with one term.
Examples: 5x2y; –8x; 16
* A Binomial is a polynomial with two terms connected by + or – signs. Examples: 7x + 10; –3x7 – 5xy2
* A Trinomial is a polynomial with three terms connected by + or – signs. Examples: 5x3 + 2x – 1; –7a + 2ab – 8b
* Any polynomial with more than three terms is simply classified as a polynomial. Example: x3 – 2x2y + 7xy2 – 8y3 (this has 4 terms)
* The degree of a term is the sum of the exponents of the variables in the term. Example: The degree of x2y3 is 2 + 3 = 5.
* The degree of a polynomial is equal to the degree of the term with the highest degree. Example: 8x5y2 + 2x3y6; The degree of 8x5y2 is 5+2 = 7. The degree of 2x3y6is 3+6 = 9. So the degree of the polynomial is 9. * The degree of a constant is zero.

Example: The constant 5 has no variable part. This term could be written as 5x0 which equals 5(1) = 5. Therefore, the degree of this term is zero. The standard form of a polynomial is when the polynomial is listed with each term in decreasing order of degree. Look at the following examples of polynomials written in standard form.

07.10 Module Seven Review and Practice Test
Addition and Subtraction of Polynomials: Lesson 07.02
To add or subtract polynomial expressions, you must combine like terms. Like terms are terms with the same exact “variable part.” Exponents for the variables must be exactly the same. To combine (add/subtract) like terms, you combine the coefficients, and the variable part stays exactly the same. For example, 3x2 + 5x2 is equal to 8x2, not 8x4. There are two methods you may use to add/subtract polynomials: * The horizontal method

* The vertical method
The steps for using the horizontal method are:
Step 1: Remove the parentheses by distributing. Recall there is actually an understood “1” in front of each polynomial.
Step 2: Identify like terms.
Step 3: Combine like terms. Be careful to consider the sign of each term! The steps for using the vertical method are:
Step 1: Remove the parentheses by distributing. Recall there is actually an understood “1” in front of each polynomial.
Step 2: Create and fill in a table.
Step 3: Combine the terms in the columns.
Check out an example using both of these methods to subtract polynomials!

Multiplication of Monomials and Polynomials: Lessons 07.03, 07.06, 07.07 When multiplying monomials and polynomials, there are “power properties” involving the base and power that may be applied. The base refers to something being raised to an exponent and the power is the exponent that the base is being raised to. basepower

Take a moment to review the following power properties.
Property| Rule| Examples|
| xmxn = x(m+n)When multiplying like bases, add the exponents| c2c5c6=c2+5+6  =c13
   
(a3b4)(a2b5)=a3+2 b4+5
 =a5b9
|
| (xm)n = x(m•n)When raising a power to another power, multiply the exponents.| (y4)5=y4•5  =y20
|
| (xy)n= xnynTo raise a product (multiplication) inside parentheses to a power, apply that power to each factor inside the parentheses.| (p3q2)4=p3•4q2•4  =p12q8
|
| x0 = 1Anything to the zero power is equal to 1.| (2x5y6z8)0 = 1| You have to be very careful with exponents and parentheses. Think hard and determine how these expressions are different. Example 1...
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