# Ch 20: Factoring

### About This Chapter

## 2014 GED Mathematical Reasoning Exam: Factoring - Chapter Summary

This chapter starts with a discussion of the purpose of factoring. Later lessons cover prime factorizations and equivalent fraction expressions. You'll also learn how to reduce fractions by dividing and factor by grouping. By the end of the chapter, you'll be ready to take the 2014 GED Mathematical Reasoning exam. Lesson topics covered in the chapter include:

- Prime factorization
- Least common multiples
- Equivalent expressions
- Fraction notation
- Factoring by grouping

This chapter on factoring contains several examples, including information on how to check your factoring work. The lessons are concise and easy to understand, with self-assessment quizzes that allow you to test your learning. These sample problems resemble the actual questions you may find on the 2014 GED Mathematical Reasoning exam.

### 2014 GED Mathematical Reasoning Exam Objectives

The updated 2014 GED exam is now entirely computer based and is designed to adhere to the Common Core State Standards. The exam seeks to assess your comprehension of common core high school academic standards in four different subjects that include mathematical reasoning. The questions on the mathematical reasoning test are divided among algebraic problem solving problems, which account for 55% of the test, and quantitative problem solving questions, which constitute 45% of the exam. The objectives of this chapter on factoring include:

- Finding the prime factorization of a number
- Using factorization to find the least common multiples
- Producing an equivalent expression by multiplying by 1
- Simplifying fraction notations
- Factoring out variables in an expression
- Reducing factors using division
- Factoring by grouping

You'll have 90 minutes to take the 2014 GED Mathematical Reasoning exam. The test is made up of multiple choice, fill-in-the-blank, hot spot and drag-and-drop questions. The mathematical reasoning exam first requires you to finish a five-question section without a calculator, then moves on to a longer second section that may be completed with the help of a computer calculator.

### 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. 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.

### 6. 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.

### 7. 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.

### 8. 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 College Algebra: Help and Review course

- Basic Arithmetic
- Overview of Real Numbers
- Foundations and Linear Equations: Help and Review
- Overview of Linear Equations
- Matrices and Absolute Value: Help and Review
- Inequalities: Help and Review
- Using FOIL, Graphing Parabolas & Solving Quadratics to Factor: Help & Review
- Properties of Polynomial Functions
- Working with Quadratic Equations
- Complex Numbers: Help and Review
- Exponents and Exponential Expressions
- Overview of Exponents
- Exponents and Polynomials: Help and Review
- Algebraic Expressions and Equations
- Rational Expressions: Help and Review
- Working with Rational Expressions
- Math Expressions and Formulas
- Functions: Help and Review
- Fractions
- Exponentials and Logarithms: Help and Review
- Probability Mechanics: Help and Review
- Calculations, Ratios & Proportions
- Percent Notation
- Data, Statistics & Probability
- Sequences and Series: Help and Review
- Basic Number Sense and Operations
- Overview of Roots & Radical Expressions
- Overview of Continuity in Mathematics
- Overview of Mathematical Limits