INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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Professor Fraser

Professor Fraser

Dividing Monomials

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Table of Contents

Section 1: Basic Concepts
Variables and Expressions

24m 5s

Intro
0:00
Definitions
0:20
Variable
0:27
Algebraic Expression
2:21
Arithmetic Operations
2:27
Lecture Example 1
7:16
Lecture Example 2
8:27
Additional Example 3
-1
Additional Example 4
-2
Order of Operations

22m 16s

Intro
0:00
Why We Need It
0:15
Example: Order of Operations
1:25
Procedure To Evaluate
3:22
Lecture Example 1
6:45
Lecture Example 2
10:55
Additional Example 3
-1
Additional Example 4
-2
The Distributive Property

16m 27s

Intro
0:00
The Distributive Property
0:20
Extension to Several Numbers
2:05
Lecture Example 1
2:50
Lecture Example 2
5:15
Additional Example 3
-1
Additional Example 4
-2
The Real Number System

22m 35s

Intro
0:00
The Real Number System
0:21
Natural Numbers
0:22
Whole Numbers
0:37
Integers
1:06
Rational Numbers
1:35
Example: Decimals
2:07
The Real Number System, Cont.
5:00
Square Roots
5:10
Principle Square Root
6:04
Irrational Numbers
6:35
The Real Number System, Cont.
9:11
Picture Representation
9:25
Lecture Example 1
11:54
Lecture Example 2
14:10
Additional Example 3
-1
Additional Example 4
-2
Functions and Graphs

27m 49s

Intro
0:00
Functions
0:30
Definition
0:30
Example: Square Roots
1:18
Example: Gas Prices
3:20
Graphs
4:03
Definition
4:03
Example: Square Roots
4:48
Domain and Range
9:30
Definition
9:30
Example: Square Roots
10:01
Lecture Example 1
11:22
Lecture Example 2
13:58
Additional Example 3
-1
Additional Example 4
-2
Section 2: Solving Linear Equations
From Sentences to Equations

22m 13s

Intro
0:00
Strategy
1:40
Using Variables
1:55
Translating Phrases
2:18
Equality
3:00
Lecture Example 1
3:52
Lecture Example 2
8:36
Additional Example 3
-1
Additional Example 4
-2
Addition and Subtraction Techniques

14m 39s

Intro
0:00
Techniques
0:22
Adding the Same Number
0:28
Example
0:47
Subtracting the Same Number
1:50
Example
1:54
Strategy
2:36
Isolate the Variable
2:46
Lecture Example 1
3:48
Lecture Example 2
5:41
Additional Example 3
-1
Additional Example 4
-2
Multiplication and Division Techniques

19m 19s

Intro
0:00
Techniques
0:16
Multiplied by the Same Number
0:18
Example
0:26
Divided by the Same Number
1:23
Non-zero Exception
1:28
Dividing by Zero
2:17
Example
3:01
Strategy
3:51
Isolate the Variable
3:55
Lecture Example 1
4:55
Lecture Example 2
6:40
Additional Example 3
-1
Additional Example 4
-2
Techniques for Multi-Step Equations

19m 13s

Intro
0:00
What are Multi-step Equations?
0:08
Strategy
0:30
Opposite Operations
0:50
Last Operation
1:18
Lecture Example 1
1:54
Lecture Example 2
4:16
Additional Example 3
-1
Additional Example 4
-2
When the Variable is on Both Sides of the Equation

24m 16s

Intro
0:00
Solving More Complicated Equations
0:17
Distributive Property and Grouping Symbols
0:36
Combining
0:51
Moving Variables to One Side
1:06
Posibble Outcomes
1:50
Exactly One Solution
2:02
No Solution
2:35
Example
2:51
Identities-True for All Real Numbers
4:26
Example
4:45
Lecture Example 1
6:17
Lecture Example 2
9:39
Additional Example 3
-1
Additional Example 4
-2
Ratios and Proportions

22m 39s

Intro
0:00
Definitions
0:16
Ratio
0:21
Proportion
0:56
Example
1:13
Cross Products
3:00
Example: Original Proportion
3:12
Example 2
5:24
Rates
6:55
Example: Gas
7:22
Example 2: Apples
7:43
Example 3: Speed
8:16
Example 4: Cookies
8:46
Lecture Example 1
9:17
Lecture Example 2
11:53
Additional Example 3
-1
Additional Example 4
-2
Applications of Percents

20m 38s

Intro
0:00
Definitions
0:22
Percent of Change
0:23
Percent of Increase
0:42
Percent of Decrease
0:55
Examples of Percent of Change
1:14
Sales Tax
1:21
Discount
1:57
Lecture Example 1
2:51
Lecture Example 2
4:46
Additional Example 3
-1
Additional Example 4
-2
More Than One Variable

22m 34s

Intro
0:00
More Than One Variable
0:21
Strategy
1:02
Typical Application
1:33
Example: Circumference
1:48
Example: Perimeter
2:21
Lecture Example 1
2:53
Lecture Example 2
5:43
Additional Example 3
-1
Additional Example 4
-2
Section 3: Functions
Relations

24m 39s

Intro
0:00
Definition
0:17
List, Table, Graph
0:42
Example: List
0:56
Example: Table
2:00
Example: Graph
2:47
Domain and Range
4:10
Inverse of a Relation
5:01
Example
5:21
Lecture Example 1
7:26
Lecture Example 2
10:39
Additional Example 3
-1
Additional Example 4
-2
Functions

19m 3s

Intro
0:00
Definition
0:21
Function
0:24
Example: Relation
0:50
Vertical Line Test
1:48
Example: Pass
2:02
Example 2: Fail
3:32
Example 3: Fail
4:18
Function Notation
5:33
Proper Notation
5:43
Example
6:29
Domain and Range
7:32
Lecture Example 1
8:06
Lecture Example 2
9:39
Additional Example 3
-1
Additional Example 4
-2
Linear Functions

20m 3s

Intro
0:00
Definition
0:12
Linear Equation
0:15
Example: A and B not zero
0:27
Example: B is zero
0:58
Example: A is zero
1:13
Graph and Intercepts
1:43
Straight Line
1:52
x-intercepts, y-intercepts
2:19
Example: Intercepts
2:27
Graphing Linear Equations
4:19
Example
4:40
Linear Functions
7:23
Example
8:00
Lecture Example 1
10:11
Lecture Example 2
12:42
Additional Example 3
-1
Additional Example 4
-2
Section 4: Linear Functions and their Graphs
Slope and Rate of Change

23m 58s

Intro
0:00
Rate of Change
0:27
Independent Variable
0:37
Dependent Variable
0:51
Slope
2:02
Example
2:19
Steepness of the Line
4:56
Possible Slopes
5:58
Positive
6:13
Negative
6:34
Zero
6:50
Undefined
7:11
Lecture Example 1
8:03
Lecture Example 2
10:34
Additional Example 3
-1
Additional Example 4
-2
Direct Variation

13m 18s

Intro
0:00
Definitions
0:13
Direct Variation
0:14
Constant of Variation
0:26
Graph
1:02
Example: Positive and Negative k
1:18
Applications
1:49
Lecture Example 1
2:16
Lecture Example 2
4:39
Additional Example 3
-1
Additional Example 4
-2
Slope Intercept Form of an Equation

17m 11s

Intro
0:00
Slope Intercept Form
0:16
Example
0:37
Lecture Example 1
2:24
Lecture Example 2
5:43
Additional Example 3
-1
Additional Example 4
-2
Point Slope Form of an Equation

10m 32s

Intro
0:00
Point Slope Form
0:11
Example
0:50
Lecture Example 1
2:03
Lecture Example 2
3:03
Additional Example 3
-1
Additional Example 4
-2
Parallel and Perpendicular Lines

18m 15s

Intro
0:00
Parallel Lines
0:12
Example: Non-vertical Lines
0:32
Perpendicular lines
1:57
Example: Slope Product is -1
2:15
Negative Reciprocal
3:08
Lecture Example 1
3:58
Lecture Example 2
7:12
Additional Example 3
-1
Additional Example 4
-2
Section 5: Systems of Equations
Graphing Systems of Equations

20m 1s

Intro
0:00
System of Equations
0:09
Definition
0:15
Solution
0:59
Solving by Graphing
1:27
Example
2:33
Number of Solutions
3:37
Independent
3:58
Dependent
4:03
Inconsistent
4:08
Example: 1 Solution
4:15
Example: No Solution
4:34
Example: Infinite Solution
4:51
Lecture Example 1
5:39
Lecture Example 2
8:51
Additional Example 3
-1
Additional Example 4
-2
Solving by Substitution

24m 12s

Intro
0:00
Substitution
0:17
Example
0:51
Number of Solutions
1:43
Infinite Solutions
2:14
No Solutions
2:50
Lecture Example 1
3:40
Lecture Example 2
6:56
Additional Example 3
-1
Additional Example 4
-2
Solving by Addition and Subtraction

12m 18s

Intro
0:00
Fundamental Principle
0:18
Adding or Subtracting
0:50
Lecture Example 1
1:23
Lecture Example 2
4:03
Additional Example 3
-1
Additional Example 4
-2
Solving by Multiplication

19m 11s

Intro
0:00
Fundamental Principle
0:24
Multiplication
0:28
Lecture Example 1
1:40
Lecture Example 2
6:36
Additional Example 3
-1
Additional Example 4
-2
Applications: Systems of Equations

18m 24s

Intro
0:00
Solving Systems of Equations
0:08
Graphing
0:32
Addition
0:50
Subtraction
1:04
Multiplication
1:13
Substitution
1:30
Lecture Example 1
3:20
Lecture Example 2
4:27
Additional Example 3
-1
Additional Example 4
-2
Section 6: Inequalities
Inequalities: Addition and Subtraction Techniques

10m 8s

Intro
0:00
Fundamental Principle
0:11
Solutions of Inequalities
0:55
Inequality
1:02
Set Builder Notation
1:13
Example
1:15
Graph on a Number Line
2:13
Lecture Example 1
3:29
Lecture Example 2
5:14
Additional Example 3
-1
Additional Example 4
-2
Inequalities: Multiplication and Division Techniques

10m 59s

Intro
0:00
Fundamental Principle
0:11
Example: Positive Number
0:51
Fundamental Principle
1:35
Example: Negative Number
1:50
Lecture Example 1
4:05
Lecture Example 2
5:12
Additional Example 3
-1
Additional Example 4
-2
Techniques for Multi-Step Inequalities

16m 21s

Intro
0:00
Similarity to Multi-step Equations
0:15
Inequalities Containing Grouping Symbols
1:03
Special Cases
1:26
Solution: All Real Numbers
1:40
Solution: Empty Set
2:16
Lecture Example 1
2:54
Lecture Example 2
4:37
Additional Example 3
-1
Additional Example 4
-2
Compound Inequalities

23m

Intro
0:00
Inequalities Combined by 'And'
0:12
Three Ways to Write Solution Set
1:41
Set Notation
2:01
Inequalities
2:12
Graph
2:29
Examples
2:31
Inequalities Combined by 'Or'
4:45
Example
5:59
Lecture Example 1
7:40
Lecture Example 2
10:55
Additional Example 3
-1
Additional Example 4
-2
Equations with Absolute Values

23m 13s

Intro
0:00
Absolute Value
0:15
Example: Distance
1:00
Absolute Value Function
2:34
Example
3:05
Lecture Example 1
4:57
Lecture Example 2
8:28
Additional Example 3
-1
Additional Example 4
-2
Inequalities with Absolute Values

17m 34s

Intro
0:00
Inequalities of the Form |x|< n
0:22
Inequalities of the Form |x|> n
3:30
Lecture Example 1
5:33
Lecture Example 2
8:50
Additional Example 3
-1
Additional Example 4
-2
Graphing Inequalities with Two Variables

30m 50s

Intro
0:00
Graph
0:22
Half-Plane
0:28
Boundary
1:37
Technique for Graphing
3:14
Example
4:01
Dashed Line
5:13
Solid Line
6:30
Technique for Graphing, cont.
8:58
Example
9:09
Lecture Example 1
12:19
Lecture Example 2
15:48
Additional Example 3
-1
Additional Example 4
-2
Graphing Systems of Inequalities

27m 38s

Intro
0:00
System of Inequalities
0:26
Example
0:43
Solving a System of Inequalities
1:17
Example
1:41
Lecture Example 1
2:58
Lecture Example 2
7:22
Additional Example 3
-1
Additional Example 4
-2
Section 7: Polynomials
Multiplying Monomials

19m 55s

Intro
0:00
What is a Monomial?
0:43
Constant
1:11
Power
1:48
Exponent and Base
2:39
Properties of Exponents
3:02
Simplified Form
5:52
Each Base Appears Exactly Once
6:02
No Powers of Powers
6:18
All Fractions Simplified
6:33
Lecture Example 1
6:43
Lecture Example 2
8:12
Additional Example 3
-1
Additional Example 4
-2
Dividing Monomials

23m 9s

Intro
0:00
Properties of Exponents
0:26
Example
1:07
Properties of Exponents, cont
2:18
Example
3:18
Properties of Exponents, cont
4:55
Example
5:32
Properties of Exponents, cont
8:49
Lecture Example 1
11:43
Lecture Example 2
13:13
Additional Example 3
-1
Additional Example 4
-2
Polynomials

16m 35s

Intro
0:00
What is a Polynomial
0:45
Monomial
0:47
Example: Trinomial
1:46
Trinomial
2:10
Example: Binomial
2:21
Binomial
2:30
Degree of a Polynomial
4:28
Example
4:40
Ordering Polynomials
6:45
Example
7:27
Lecture Example 1
9:27
Lecture Example 2
10:31
Additional Example 3
-1
Additional Example 4
-2
Adding and Subtracting Polynomials

22m

Intro
0:00
Adding Polynomials
0:36
Like Polynomials
0:48
Example
1:04
Subtracting Polynomials
3:55
Example
4:01
Lecture Example 1
5:30
Lecture Example 2
8:04
Additional Example 3
-1
Additional Example 4
-2
Multiplying Polynomials by Monomials

24m 8s

Intro
0:00
Distributive Property
0:22
Basic Principle
0:42
Example
1:04
Solving Equations
3:25
Lecture Example 1
4:26
Lecture Example 2
7:51
Additional Example 3
-1
Additional Example 4
-2
Multiplying Polynomials

26m 37s

Intro
0:00
Distributive Property
0:23
Example
0:34
Example
1:55
Foil Method
5:17
Lecture Example 1
7:44
Lecture Example 2
10:15
Additional Example 3
-1
Additional Example 4
-2
Special Products

19m 40s

Intro
0:00
Square of a Sum
0:12
Perfect Square Trinomial
1:43
Example
2:13
FOIL Technique
3:09
Square of a Difference
3:38
Example
5:27
Difference of Two Squares
6:12
Example
7:43
Lecture Example 1
8:51
Lecture Example 2
11:06
Additional Example 3
-1
Additional Example 4
-2
Section 8: Factoring
Factoring Monomials

27m 25s

Intro
0:00
Prime and Composite Numbers
1:01
Prime Number
1:23
Composite Number
3:03
Factored Forms
4:07
Prime Factored Form
4:19
Factored Form
5:40
Greatest Common Factor (GCF)
7:41
Example
8:00
GCF of Monomials
10:07
Example
10:18
Lecture Example 1
12:52
Lecture Example 2
17:08
Additional Example 3
-1
Additional Example 4
-2
Factoring Using Greatest Common Factor (GCF)

26m 3s

Intro
0:00
Distributive Property
0:19
Factor Out an Expression
1:21
Example
2:52
Factoring by Grouping
4:40
Example
6:00
Zero Product Property
8:24
Example
9:03
Lecture Example 1
11:19
Lecture Example 2
14:19
Additional Example 3
-1
Additional Example 4
-2
Factoring Trinomials with Leading Coefficient 1

27m 37s

Intro
0:00
Factoring Trinomials
0:23
Example
2:06
Rules for Signs
6:27
Both Positive
6:41
Both Negative
7:00
Opposite Signs
7:33
Solving Equations
8:26
Example
8:59
Lecture Example 1
11:14
Lecture Example 2
14:01
Additional Example 3
-1
Additional Example 4
-2
Factoring General Trinomials

34m 11s

Intro
0:00
Factoring Trinomials
0:40
Example: List
1:38
Grouping
5:46
Example
5:55
Rules for Signs
9:04
Example
9:22
Greatest Common Factor (GCF)
10:29
Prime Polynomials
11:03
Example
11:32
Solving Equations
12:32
Lecture Example 1
13:11
Lecture Example 2
18:37
Additional Example 3
-1
Additional Example 4
-2
Factoring the Difference of Two Squares

20m 22s

Intro
0:00
Difference of Two Squares
0:40
Example
1:56
Factoring Using Several Techniques
3:33
Solving Equations
4:11
Lecture Example 1
4:55
Lecture Example 2
6:05
Additional Example 3
-1
Additional Example 4
-2
Factoring Perfect Squares

18m 7s

Intro
0:00
Perfect Squares
0:10
Perfect Square Trinomials
1:17
Solving Equations
2:53
Square Root Property
2:58
Example
3:06
Lecture Example 1
4:23
Lecture Example 2
6:56
Additional Example 3
-1
Additional Example 4
-2
Section 9: Quadratic Functions
Graphing Quadratic Functions

28m 5s

Intro
0:00
Parabolas
0:09
Parabolas That Open Upward
3:58
Minimum
4:26
Parabolas That Open Downward
4:54
Maximum
5:09
Vertex
7:28
Example
8:01
Axis of Symmetry
11:03
Lecture Example 1
13:27
Lecture Example 2
17:17
Additional Example 3
-1
Additional Example 4
-2
Solving Equations by Graphing

28m 18s

Intro
0:00
Solving a Quadratic Equation
0:22
Example
0:50
Two Distinct Solutions/Roots
5:08
One Double Root
5:58
No Real Roots
7:14
Estimating Solutions
8:00
Example
8:16
Example
8:31
Lecture Example 1
9:43
Lecture Example 2
14:10
Additional Example 3
-1
Additional Example 4
-2
Solving Equations by Completing the Square

25m 7s

Intro
0:00
Perfect Square Trinomials
0:22
Example
1:12
Completing the Square
3:17
Example
3:25
Solving Equations
6:12
Example
6:27
Leading Coefficient is 1
8:25
Lecture Example 1
10:23
Lecture Example 2
14:17
Additional Example 3
-1
Additional Example 4
-2
Solving Equations Using the Quadratic Formula

24m 15s

Intro
0:00
Quadratic Formula
1:26
Example
2:23
Discriminant
4:28
Two Distinct Real Roots
5:07
One Double Real Root
5:23
No Real Root
5:42
Why Does It Work?
6:05
Lecture Example 1
7:53
Lecture Example 2
11:50
Additional Example 3
-1
Additional Example 4
-2
Section 10: Radical Expressions and Equations
Simplifying Radical Expressions

32m 40s

Intro
0:00
Radical Expressions
0:14
Radicand
0:28
Example
0:32
Simplest Form
1:07
Example
1:35
Product Property
2:34
Verifications
2:47
Square Roots of Variables with Even Powers
4:27
Quotient Rule
6:45
Example
6:55
Rationalizing Denominators
7:32
Example
7:41
Conjugates
10:44
Examples
10:59
Simplest Radical Form
14:44
Example
15:39
Lecture Example 1
17:34
Lecture Example 2
19:38
Additional Example 3
-1
Additional Example 4
-2
Operations with Radical Expressions

19m 59s

Intro
0:00
Adding and Subtracting Radical Expressions
0:12
Example
0:19
Multiplying Radical Expressions
1:53
Example
2:07
Lecture Example 1
5:29
Lecture Example 2
6:36
Additional Example 3
-1
Additional Example 4
-2
Solving Radical Equations

26m 50s

Intro
0:00
Radical Equations
0:22
Example
0:33
Solving a Radical Equation
2:04
Example
2:16
Extraneous Solutions
3:14
Example
4:31
Lecture Example 1
7:33
Lecture Example 2
9:45
Additional Example 3
-1
Additional Example 4
-2
Pythagorean Theorem

19m 8s

Intro
0:00
Right Triangles
0:51
Right Angle
1:03
Vertex
1:11
Symbol
1:16
Hypotenuse and Legs
1:42
Pythagorean Theorem
2:27
Example
2:47
Example
3:12
Pythagorean Triples
4:03
Converse of the Pythagorean Theorem
6:39
Example
7:41
Lecture Example 1
8:57
Lecture Example 2
10:05
Additional Example 3
-1
Additional Example 4
-2
Distance Formula

18m 27s

Intro
0:00
Distance Formula
0:17
Missing Coordinates
1:46
Example
1:55
Lecture Example 1
4:10
Lecture Example 2
5:57
Additional Example 3
-1
Additional Example 4
-2
Section 11: Rational Expressions and Equations
Inverse Variation

14m 43s

Intro
0:00
Inverse Variation
0:23
Constant of Variation
0:37
Graphing Inverse Variation
1:08
Example: Hyperbola
1:15
Product Rule
3:54
Lecture Example 1
5:31
Lecture Example 2
7:43
Additional Example 3
-1
Additional Example 4
-2
Rational Expressions

32m 43s

Intro
0:00
Rational Expression
0:55
Example
1:03
Excluded Values
1:29
Examples
1:40
Simplifying Rational Expressions
5:36
Greatest Common Factor (GCF)
5:46
Example
5:55
Example
7:42
Simplifying and Excluded Values
9:34
Lecture Example 1
9:50
Lecture Example 2
13:55
Additional Example 3
-1
Additional Example 4
-2
Multiplying Rational Expressions

27m 22s

Intro
0:00
Procedure
0:16
Example
0:33
Cancel Before Multiplication
3:44
Example
3:55
Rational Expressions Containing Polynomials
6:19
Example
6:26
Lecture Example 1
11:09
Lecture Example 2
15:39
Additional Example 3
-1
Additional Example 4
-2
Dividing Rational Expressions

28m 30s

Intro
0:00
Procedure
0:21
Example
0:59
Cancel Before Multiplication
4:31
Example
4:39
Rational Expressions Containing Polynomials
8:01
Example
8:08
Lecture Example 1
10:43
Lecture Example 2
13:46
Additional Example 3
-1
Additional Example 4
-2
Dividing Polynomials

29m 44s

Intro
0:00
Dividing a Polynomial by a Monomial
1:07
Example
1:14
Dividing a Polynomial by a Binomial
3:30
Example
3:51
Long Division
5:20
Example
6:25
Missing Terms
11:11
Example
12:25
Lecture Example 1
14:54
Lecture Example 2
16:35
Additional Example 3
-1
Additional Example 4
-2
Adding and Subtracting Rational Expressions with Like Denominators

16m 50s

Intro
0:00
Adding with Like Denominators
0:14
Example
0:41
Subtraction with Like Denominators
2:23
Example
2:30
Denominators That Are Additive Inverses
2:55
Example
3:03
Lecture Example 1
6:41
Lecture Example 2
7:09
Additional Example 3
-1
Additional Example 4
-2
Adding and Subtracting Rational Expressions with Unlike Denominators

36m

Intro
0:00
Least Common Multiple (LCM) of Polynomials
0:34
Example
0:45
Example
1:55
Adding and Subtracting
4:08
Example
4:45
Lecture Example 1
8:13
Lecture Example 2
10:22
Additional Example 3
-1
Additional Example 4
-2
Complex Fractions

18m 43s

Intro
0:00
Mixed Expression
0:08
Example
0:30
Complex Fraction
2:45
Example
2:57
Example
3:11
Example
3:22
Simplifying Complex Fractions
3:58
Why Does It Work?
4:22
Lecture Example 1
4:48
Lecture Example 2
8:44
Additional Example 3
-1
Additional Example 4
-2
Rational Equations

39m 10s

Intro
0:00
Definition
0:08
Examples
0:17
Solving Rational Expressions
3:02
Example
3:09
Work Problems
6:31
Example
6:48
Extraneous Solutions
13:12
Example
14:13
Lecture Example 1
17:21
Lecture Example 2
19:59
Additional Example 3
-1
Additional Example 4
-2
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