# Ch 11: Algebra II: Factoring

### About This Chapter

## Algebra II: Factoring - Chapter Summary and Learning Objectives

This chapter starts with a definition of factoring and its relation to algebra. You'll learn how to use factorization and fraction notation to solve equations. You'll also study how to transform factoring into a division problem. By the end of the chapter, you should understand:

- Prime factorization
- Least common multiples
- Equivalent expressions
- Fraction notation
- Factoring transformations
- Factoring by grouping
- Rational roots theorem

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

What Is Factoring in Algebra? - Definition and Example | Provide a definition of factoring and explain its purpose in algebra. Define important algebraic terms like factors, coefficients and constants. |

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

Using Prime Factorizations to Find the Least Common Multiples | Determine the least common multiples of two or more numbers using prime factorization techniques. |

Equivalent Expressions and Fraction Notation | Find equivalent fraction expressions by multiplying by 1. |

Using Fraction Notation: Addition, Subtraction, Multiplication and Division | Perform basic addition, subtraction, multiplication and division operations using fraction notation. |

Factoring Out Variables: Instruction and Examples | Factor out the variables in an expression and provide several examples. |

Combining Numbers and Variables When Factoring | Learn how to combine numbers and variables when factoring to find the greatest common factor. |

Transforming Factoring into a Division Problem | Explain how to reduce fractions using division operations to make equations easier to solve. |

Factoring by Grouping: Steps, Verification and Examples | Recognize the steps needed to factor by grouping and understand how to verify your answer. |

How to Use the Rational Roots Theorem: Process and Examples | Understand how to use the rational roots theorem and provide sample math problems. |

### 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.

### 10. How to Use the Rational Roots Theorem: Process & Examples

When it comes to solving polynomials, it can sometimes be easier to begin with a list of possible solutions to try. This video lesson tells you how to form a list of possible solutions by using the rational roots theorem.

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### Other Chapters

Other chapters within the Algebra II: High School course

- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Homeschool Resources for High School Algebra II