Math - How to Factor

Name: Math - How to Factor
Rating: 4.7 (230 reviews)

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

Created byChris Wingard

Last updated 5/2015

English

What you'll 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

Course content

8 sections • 45 lectures • 2h 8m total length

Topic Outline1:43
This is a brief outline of the topics that will be discussed in this course.

Factor Trees1:55
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.
So What Exactly is the Greatest Common Factor?1:27
Before we start finding GCFs, we should make sure we talk about what they are.
Example 1 - Two Numbers1:52
An explanation of how to find the GCF of two numbers, along with an example.
Example 2 - Two Numbers2:05
Another example of finding the GCF of two numbers.
Example 3 - Three Numbers3:14
An example of finding the GCF of three numbers. It's just like two but with one more number to factor.
Section 2 Review and Review Answers2:00
Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

What's an Algebraic Expression?1:30
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 the GCF of an Algebraic Expression?1:13
This lecture explains what the greatest common factor of an algebraic expression is.
Example 1 - One Variable3:30
An example of finding the GCF of an algebraic expression that involves only one variable.
Example 2 - Two Variables5:38
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 3 - Two Variables3:28
Another example of finding the GCF of an algebraic expression with two variables.
Example 4 - Three Variables5:01
An example of finding the GCF of an algebraic expression with three variables.
Section 3 Review and Review Answers2:00
Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

What Exactly is Factoring?1:50
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.
Example 1 - One Variable3:04
An example of using the GCF to factor an algebraic expression that has one variable.
Example 2 - One Variable2:33
An example of using the GCF to factor an algebraic expression that has two variables.
Example 3 - Two Variables2:56
Another example of using the GCF to factor an algebraic expression that has two variables.
Example 4 - Three Variables3:54
An example of using the GCF to factor an algebraic expression that has three variables.
Section 4 Review and Review Answers2:00
Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

Sum of Cubes - Formula and Explanation3:08
A brief explanation/verification of the formula for factoring a sum of cubes.
Example 1 - Factoring a Sum of Cubes2:08
An explanation and example of how to factor a sum of cubes.
Example 2 - Factoring a Sum of Cubes3:56
An example of factoring a more complicated sum of cubes.
Difference of Cubes - Formula and Explanation2:25
A brief explanation/verification of the formula for factoring a difference of cubes.
Example 3 - Factoring a Difference of Cubes2:30
An explanation and example of how to factor a difference of cubes.
Example 4 - Factoring a Difference of Cubes4:37
An example of factoring a more complicated difference of cubes.
Difference of Squares - Formula and Explanation2:45
A brief explanation/verification of the formula for factoring a difference of squares.
Example 5 - Factoring a Difference of Squares1:23
An explanation and example of how to factor a difference of squares.
Example 6 - Factoring a Difference of Squares3:07
An example of factoring a more complicated difference of squares.
Section 6 Review and Review Answers3:00
Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

What's a Quadratic Expression?3:05
A brief explanation of what a quadratic expression is, including an explanation of what "leading coefficient" means.
Example 12:43
An explanation and example of factoring a quadratic expression.
Why do we do it the Way we do it?3:13
This lecture explains why we factor quadratics the way that we do.
Example 22:46
Another example of factoring a quadratic expression.
Example 33:00
Another example of factoring a quadratic expression.
Example 42:18
Another example of factoring a quadratic expression.
Section 7 Review and Review Answers2:00
Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

Example 17:57
An explanation and example of factoring a more complicated quadratic expression.
Example 25:31
Another example of factoring a more complicated quadratic expression.
Example 36:19
Another example of factoring a more complicated quadratic expression.
Example 45:34
Another example of factoring a more complicated quadratic expression.
Section 8 Review and Review Answers2:00
Use the attached review problems to check your understanding of the topics in this section. Answers are in the other attached document.

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 this course is for:

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

Math - How to Factor

What you'll learn

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Course content

Introduction1 lecture • 2min

Finding the GCF of Numbers6 lectures • 13min

Finding the GCF of Algebraic Expressions7 lectures • 22min

Using the GCF to Factor Algebraic Expressions6 lectures • 16min

Factoring by Grouping3 lectures • 14min

Factoring Special Types of Algebraic Expressions10 lectures • 29min

Factoring Quadratic Expressions - Part 1 of 27 lectures • 19min

Factoring Quadratic Expressions - Part 2 of 25 lectures • 27min

Requirements

Description

Who this course is for: