# Ch 13: High School Algebra: Factoring

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### About This Chapter

## Factoring - Chapter Summary and Learning Objectives

This chapter helps you understand the definitions for factor, coefficient, relatively prime and constant. Here our instructors will train you in the different ways factoring is used in real life and algebra. By the time you finish the video lessons, you should know the various ways factors are used to make a multiplication expression. Concepts covered during this chapter include how to:

- Find the prime factorization of a number
- Explain how to use grouping to factor
- Simplify fraction notation
- Use fraction notion when adding, subtracting, dividing and multiplying
- Combine variables and numbers
- Factor out terms in an expression

Video | Objective |
---|---|

What is Factoring and Why Do We Do It? | Define factoring and discuss its purpose in algebra (and real life). Define terms used when discussing factoring, such as term, factor, coefficient, constant and relatively prime. |

How to Find the Prime Factorization of a Number | Learn how to find the prime factorization of a number. |

Using Prime Factorizations to Find the Least Common Multiples | Explain how to find the LCM of two or more numbers using prime factorization. |

Equivalent Expressions and Fraction Notation | Explain how to find equivalent fraction expressions by multiplying by one. Demonstrate how to simplify fraction notation. |

Using Fraction Notation | Demonstrate how to add, subtract, multiply and divide using fraction notation. |

Factoring Out Variables | Describe how to factor out the terms in an expression, including variables and numbers. |

Combining Numbers and Variables When Factoring | Explain how to combine numbers and variables, find the GCF and factor an expression. |

Transforming Factoring into a Division Problem | Describe how to reduce fractions using division to make computations easier when factoring. |

Factoring By Grouping | Explain how to use grouping to factor and detail each step in the process. |

### 1. What is Factoring in Algebra? - Definition & Example

Factoring with ordinary numbers involves knowing that 6 is the product of 2 and 3. But what about factoring in algebra? In this lesson, we'll learn the essential elements of algebra factoring.

### 2. How to Find the Prime Factorization of a Number

The prime factorization of a number involves breaking that number down to its smallest parts. This lesson will show you two different ways to discover the prime factorization of any number.

### 3. Using Prime Factorizations to Find the Least Common Multiples

Finding the least common multiple can seem like a lot of work. But we can use prime factorization as a shortcut. Find out how and practice finding least common multiples in this lesson.

### 4. Equivalent Expressions and Fraction Notation

Did you know that two fractions can look completely different, but actually be the same? In this lesson, we'll learn about equivalent fractions. We'll also learn to simplify fraction notation.

### 5. Using Fraction Notation: Addition, Subtraction, Multiplication & Division

How do we add, subtract, multiply or divide with fractions? In this lesson, we'll learn how to use fraction notation correctly no matter what operation we're completing.

### 6. Factoring Out Variables: Instructions & Examples

Let's find the factors. In this lesson, we'll learn how to factor out numbers or variables from an expression. We'll even learn how to factor variables with exponents.

### 7. Combining Numbers and Variables When Factoring

With an expression, you know how to factor out a number, and you know how to factor out a variable. In this lesson, we'll learn how to factor out combined numbers and variables.

### 8. Transforming Factoring Into A Division Problem

Watch this video lesson to learn how you can factor a problem by turning it into a division problem. Learn how this actually helps you to factor and keep your numbers straight.

### 9. Factoring By Grouping: Steps, Verification & Examples

How do you factor an expression if all the terms don't share a common factor? Grouping! In this lesson, we'll learn how to use grouping to help factor expressions.

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### Other Chapters

Other chapters within the Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Linear Equations
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability
- Teacher Resources for High School Algebra