# Ch 3: NYSTCE Mathematics: Factoring & Divisibility

### About This Chapter

## NYSTCE Mathematics: Factoring & Divisibility - Chapter Summary

If it's almost time to sit for the NYSTCE Mathematics examination, take the time to brush up on your math skills. The professionally-developed text and video lessons in this chapter explain the intricate processes of factoring and divisibility in algebra. Review the steps required for combining variables and multiplying factors, and recall how to use the greatest common factor to create fractions from polynomials. A number of examples will walk you through the process of finding factors and simplifying fraction notation. You can expect this chapter to help you with:

- Defining factoring and factor pairs
- Developing factoring teaching strategies
- Calculating the factor and multiple of a whole number
- Solving equivalent fractions
- Explaining how to factor out variables and combined numbers
- Transforming a fraction equation into a division problem
- Using the grouping process to factor
- Listing the numbers that are divisible by 2, 3, 4, 5, 6, 7, 8, 9 and 10

The online text and video lessons are taught by credentialed math educators. Key terms will show up on screen, and they're featured in bold text in the lesson transcripts. To facilitate the learning process, you'll be able to adjust the volume, instantly pause the lessons, switch to full-screen mode, ask questions of math experts and print out worksheets that contain your corrected quiz answers.

### 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. What Is a Factor Pair?

In this lesson, we'll review factors and products before learning about factor pairs. We'll then view a few examples of finding the factor pairs of different products. After, you can test your knowledge in a brief quiz.

### 3. Finding Factors of Whole Numbers

After watching this video lesson, you will be able to factor any whole number that you are given. You will learn what factors are and how a whole number can have several different factors.

### 4. Finding Multiples of Whole Numbers

After watching this video lesson, you will become a pro at finding multiples of whole numbers. Learn what they are and how you can visualize the process to make it easier for you.

### 5. 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.

### 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. Divisibility by 2, 3, and 4

In this video lesson, you will learn what it means to be divisible. Also, you'll see what numbers are divisible by 2, 3, and 4. You will also learn how you can check if something is divisible by these numbers.

### 11. Divisibility by 5, 6, and 7

In this video lesson, we will see what numbers can be divided equally by 5, 6, and 7. Learn the pattern that you can use to find other numbers divisible by 5, 6 and 7. Learn how you can visualize divisibility.

### 12. Divisibility by 8, 9, and 10

In this video lesson, we will see what numbers are divisible by 8, 9, and 10. You will learn how you can figure out these numbers yourself. Learn what it means to be divisible.

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### Other Chapters

Other chapters within the NYSTCE Mathematics (004): Practice & Study Guide course

- NYSTCE Mathematics: Fractions, Decimals & Percents
- NYSTCE Mathematics: Complex Numbers
- NYSTCE Mathematics: Exponents
- NYSTCE Mathematics: Patterns & Functions
- NYSTCE Mathematics: Understanding Algebraic Expressions
- NYSTCE Mathematics: Solving Algebraic Equations
- NYSTCE Mathematics: Linear Equations
- NYSTCE Mathematics: Quadratic Functions
- NYSTCE Mathematics: Polynomial Functions
- NYSTCE Mathematics: Exponential Expressions
- NYSTCE Mathematics: Absolute Value Expressions
- NYSTCE Mathematics: Rational Expressions
- NYSTCE Mathematics: Radical Expressions
- NYSTCE Mathematics: Exponential & Logarithmic Functions
- NYSTCE Mathematics: Trigonometry
- NYSTCE Mathematics: Applications of Trigonometry
- NYSTCE Mathematics: Calculus Concepts
- NYSTCE Mathematics: Calculus Applications
- NYSTCE Mathematics: Principles of Measurement
- NYSTCE Mathematics: Lines & Angles
- NYSTCE Mathematics: Parallel Lines & Symmetry
- NYSTCE Mathematics: Geometric Construction
- NYSTCE Mathematics: Geometric Shapes
- NYSTCE Mathematics: Triangle Proofs & Theorems
- NYSTCE Mathematics: Geometric Solids
- NYSTCE Mathematics: Conic Sections
- NYSTCE Mathematics: Vector Operations
- NYSTCE Mathematics: Transformations in Geometry
- NYSTCE Mathematics: Coordinate Geometry
- NYSTCE Mathematics: Sequences & Series
- NYSTCE Mathematics: Counting Strategies
- NYSTCE Mathematics: Probability
- NYSTCE Mathematics: Probability Distributions
- NYSTCE Mathematics: Data Analysis & Statistics
- NYSTCE Mathematics: Sampling & Prediction
- NYSTCE Mathematics: Regression & Correlation
- NYSTCE Mathematics: Discrete Mathematics
- NYSTCE Mathematics Flashcards