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Learn how to factor algebraic expressions, including the infamous and dreaded quadratic expressions!

3,211 students enrolled

- 2 hours on-demand video
- 7 Supplemental Resources
- Full lifetime access
- Access on mobile and TV

- Certificate of Completion

What Will I Learn?

- Find the greatest common factor (GCF) of two or more numbers
- Find the GCF of algebraic expressions
- Use the GCF to factor algebraic expressions
- Factor algebraic expressions by grouping
- Identify and factor special types of algebraic expressions
- Factor quadratic expressions

Requirements

- Have basic arithmetic skills
- Know what a variable is
- Know the basic rules of exponents
- It helps to know what an algebraic expression is, but if you don't, don't worry! It's very simple and we'll review the definition when it is first needed.

Description

Taught by a former college math instructor with over 8 years of experience teaching and over 14 years of experience tutoring.

This course will teach you how to factor with the GCF (greatest common factor), how to factor by grouping, how to factor special types of expressions, and most importantly, how to factor the well-known-but-not-so-well-liked quadratic expression.

We begin with an outline of the topics to be discussed, then we jump right in with explanations and examples. Each section has explanations, examples, and review worksheets with full solutions. The solutions are provided in separate documents so you can do the worksheets without having the answers in front of you. Sort of like a mini self-quiz.

Why take this course? It will make your life significantly easier in your math classes, leading to an easier life in general. Factoring is one of the most important concepts taught in math at this level. It is widely used in more advanced math classes for things like solving equations and performing other, more advanced operations. Please trust me when I say that your future math courses - and even your current course later on - will be very difficult if you do not have adequate factoring skills. I have seen it myself too many times. Students in more advanced courses like precalculus and calculus (and beyond) struggle with the concepts early on in those courses because they don't have a solid background in the basics, including and especially factoring. I can't count how often I've seen this, and I'm usually pretty good at counting stuff.

But really, it's an important skill to have, and an absolutely indispensable one if you are planning to continue taking courses in math.

Who is the target audience?

- Algebra or Precalculus students, whether in high school or college
- Students in more advanced courses who need a refresher

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Curriculum For This Course

45 Lectures

02:22:44
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Introduction
1 Lecture
01:43

This is a brief outline of the topics that will be discussed in this course.

Topic Outline

01:43

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Finding the GCF of Numbers
6 Lectures
10:33

An explanation of what factor trees are, since we will be using them to find the GCF in the examples that follow. This is likely to be review, but if it isn't, don't worry! It's not a difficult concept to understand.

Factor Trees

01:55

Before we start finding GCFs, we should make sure we talk about what they are.

So What Exactly is the Greatest Common Factor?

01:27

An explanation of how to find the GCF of two numbers, along with an example.

Example 1 - Two Numbers

01:52

Another example of finding the GCF of two numbers.

Example 2 - Two Numbers

02:05

An example of finding the GCF of three numbers. It's just like two but with one more number to factor.

Example 3 - Three Numbers

03:14

Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

Section 2 Review and Review Answers

2 pages

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Finding the GCF of Algebraic Expressions
7 Lectures
20:20

A brief explanation of what an algebraic expression is. Chances are you already know what this is, although you may know and refer to it by a different name.

What's an Algebraic Expression?

01:30

This lecture explains what the greatest common factor of an algebraic expression is.

What's the GCF of an Algebraic Expression?

01:13

An example of finding the GCF of an algebraic expression that involves only one variable.

Example 1 - One Variable

03:30

An example of finding the GCF of an algebraic expression with two variables. This lecture also covers a shortcut technique to use when the powers of the variables are inconveniently large.

Example 2 - Two Variables

05:38

Another example of finding the GCF of an algebraic expression with two variables.

Example 3 - Two Variables

03:28

An example of finding the GCF of an algebraic expression with three variables.

Example 4 - Three Variables

05:01

Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

Section 3 Review and Review Answers

2 pages

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Using the GCF to Factor Algebraic Expressions
6 Lectures
14:17

An explanation of what factoring is. If you're enrolled in this course you likely already know what factoring is, but my experience has been that most people don't think of it the way I discuss in this video.

What Exactly is Factoring?

01:50

An example of using the GCF to factor an algebraic expression that has one variable.

Example 1 - One Variable

03:04

An example of using the GCF to factor an algebraic expression that has two variables.

Example 2 - One Variable

02:33

Another example of using the GCF to factor an algebraic expression that has two variables.

Example 3 - Two Variables

02:56

An example of using the GCF to factor an algebraic expression that has three variables.

Example 4 - Three Variables

03:54

Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

Section 4 Review and Review Answers

2 pages

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Factoring by Grouping
3 Lectures
13:26

An explanation and example of factoring by grouping. The algebraic expression has one variable.

Example 1

08:24

Another example of factoring by grouping. The algebraic expression has one variable.

Example 2

05:02

Section 5 Review and Review Answers

1 page

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Factoring Special Types of Algebraic Expressions
10 Lectures
25:59

A brief explanation/verification of the formula for factoring a sum of cubes.

Sum of Cubes - Formula and Explanation

03:08

An explanation and example of how to factor a sum of cubes.

Example 1 - Factoring a Sum of Cubes

02:08

An example of factoring a more complicated sum of cubes.

Example 2 - Factoring a Sum of Cubes

03:56

A brief explanation/verification of the formula for factoring a difference of cubes.

Difference of Cubes - Formula and Explanation

02:25

An explanation and example of how to factor a difference of cubes.

Example 3 - Factoring a Difference of Cubes

02:30

An example of factoring a more complicated difference of cubes.

Example 4 - Factoring a Difference of Cubes

04:37

A brief explanation/verification of the formula for factoring a difference of squares.

Difference of Squares - Formula and Explanation

02:45

An explanation and example of how to factor a difference of squares.

Example 5 - Factoring a Difference of Squares

01:23

An example of factoring a more complicated difference of squares.

Example 6 - Factoring a Difference of Squares

03:07

Section 6 Review and Review Answers

3 pages

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Factoring Quadratic Expressions - Part 1 of 2
7 Lectures
17:05

A brief explanation of what a quadratic expression is, including an explanation of what "leading coefficient" means.

What's a Quadratic Expression?

03:05

An explanation and example of factoring a quadratic expression.

Example 1

02:43

This lecture explains why we factor quadratics the way that we do.

Why do we do it the Way we do it?

03:13

Another example of factoring a quadratic expression.

Example 2

02:46

Another example of factoring a quadratic expression.

Example 3

03:00

Another example of factoring a quadratic expression.

Example 4

02:18

Section 7 Review and Review Answers

2 pages

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Factoring Quadratic Expressions - Part 2 of 2
5 Lectures
25:21

An explanation and example of factoring a more complicated quadratic expression.

Example 1

07:57

Another example of factoring a more complicated quadratic expression.

Example 2

05:31

Another example of factoring a more complicated quadratic expression.

Example 3

06:19

Another example of factoring a more complicated quadratic expression.

Example 4

05:34

Section 8 Review and Review Answers

2 pages

About the Instructor

Math Guy, Database Programmer

Chris is a full-time programmer analyst for a retirement organization. He insists it's more fun than it sounds. He is also a part-time math teacher at the local community college. Several years and 30 pounds ago, he was a full-time university math teacher.

Since 2007 he has taught courses ranging from Intermediate Algebra to Differential Equations, with class sizes varying from 6 to over 200 students. He has been tutoring math in person and online since 2000.

His educational background includes undergraduate Ivy League degrees in math and computer science, two master's degrees in math (one for "real" and one for "fun"), and an in-progress master's degree in computer science.

When not doing work stuff, Chris enjoys reading, playing the guitar and piano, eating, exercising to balance out the eating, traveling, Netflix, video games, and hanging out with his girlfriend and their cats. Six cats. So many cats.

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