Math - How to Factor

Learn how to factor algebraic expressions, including the infamous and dreaded quadratic expressions!
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Instructed by Chris W Academics / Math & Science
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  • Lectures 45
  • Contents Video: 2 hours
    Other: 14 mins
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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About This Course

Published 5/2015 English

Course 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.

What are the 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.

What am I going to get from this course?

  • 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

What is the target audience?

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

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

Section 1: Introduction
01:43

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

Section 2: Finding the GCF of Numbers
01:55

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.

01:27

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

01:52

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

02:05

Another example of finding the GCF of two numbers.

03:14

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

2 pages

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

Section 3: Finding the GCF of Algebraic Expressions
01:30

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.

01:13

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

03:30

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

05:38

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.

03:28

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

05:01

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

2 pages

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

Section 4: Using the GCF to Factor Algebraic Expressions
01:50

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.

03:04

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

02:33

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

02:56

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

03:54

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

2 pages

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

Section 5: Factoring by Grouping
08:24

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

05:02

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

1 page

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

Section 6: Factoring Special Types of Algebraic Expressions
03:08

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

02:08

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

03:56

An example of factoring a more complicated sum of cubes.

02:25

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

02:30

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

04:37

An example of factoring a more complicated difference of cubes.

02:45

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

01:23

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

03:07

An example of factoring a more complicated difference of squares.

3 pages

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

Section 7: Factoring Quadratic Expressions - Part 1 of 2
03:05

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

02:43

An explanation and example of factoring a quadratic expression.

03:13

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

02:46

Another example of factoring a quadratic expression.

03:00

Another example of factoring a quadratic expression.

02:18

Another example of factoring a quadratic expression.

2 pages

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

Section 8: Factoring Quadratic Expressions - Part 2 of 2
07:57

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

05:31

Another example of factoring a more complicated quadratic expression.

06:19

Another example of factoring a more complicated quadratic expression.

05:34

Another example of factoring a more complicated quadratic expression.

2 pages

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

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Instructor Biography

Chris W, Mathematician, Computer Programmer, Tutor

Former math teacher with 8+ years of experience teaching college math courses ranging from Intermediate Algebra to Calculus II, with class sizes varying from 2 to over 200 students. I also have over 14 years of experience tutoring math.

As time went on, teaching was becoming more administrative and less academic. Eventually I left and pursued a different career path. I keep up with teaching through my videos and educational apps. This allows me to focus on the part of teaching I enjoy the most - the actual teaching.

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