# Ch 12: Compass Math: Monomials & Polynomials

### About This Chapter

## ACT Compass Math: Monomials & Polynomials - Chapter Summary

Become more familiar with several key Compass Math content pieces, like the binomial theorem, that can be studied across the lessons. You will also see all of the following topics in the chapter to give you a strong and broad understanding of monomials and polynomials:

- Adding, subtracting, multiplying and dividing monomials
- Cube and square roots
- Evaluating a polynomial in function notation
- How to use synthetic and long division to divide polynomials
- Polynomials with several variables
- Understanding basic polynomial graphs
- Graphing cubics, quartics and quintics
- Pascal's triangle

The short videos and information-packed transcripts will highlight the fundamentals of monomials and polynomials. The practice quizzes with each lesson give you instant feedback on what you've been learning as you go through the chapter.

### Objectives of the ACT Compass Math: Monomials & Polynomials Chapter

The ACT Compass Math Test's questions dealing with the information in this chapter are in the Math Diagnostics Test as well as in the Math Placement Test. This chapter aims to make you comfortable with any test question on definitions and operations related to monomials and polynomials. The ACT Compass Math test has multiple-choice type questions, just like the format of the practice questions in the Monomials & Polynomials chapter.

### 1. What Are Monomials & Polynomials?

Watch this video lesson to learn how coefficients and variables combine to form monomials and polynomials. You'll also find out how the exponent determines the degree of polynomials.

### 2. How to Add & Subtract Monomials

In this video lesson, you will learn what kinds of monomials you can add or subtract together. You will also learn how to immediately tell when you cannot add or subtract your monomials.

### 3. How to Multiply & Divide Monomials

In this lesson, we're going to learn how to multiply and divide monomials. As you can imagine, this is a very important skill that much of algebra (and even more advanced math) depends upon.

### 4. Square & Cube Roots of Monomials

Being able to find the cube or square root of monomials can make all math much easier, and it's not as hard as you'd think. This lesson will show you how and allow you to test your skills with a quiz.

### 5. How to Evaluate a Polynomial in Function Notation

This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.

### 6. Understanding Basic Polynomial Graphs

This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.

### 7. Basic Transformations of Polynomial Graphs

The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.

### 8. How to Graph Cubics, Quartics, Quintics and Beyond

Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!

### 9. How to Add, Subtract and Multiply Polynomials

Adding, subtracting and multiplying polynomials are, basically, the same as adding, subtracting and multiplying numbers. They only difference is that we have a pesky variable to worry about, but this video will show you that's no problem, so no worries! This method has worked for many of my students, and I think it will work for you, too!

### 10. Pascal's Triangle: Definition and Use with Polynomials

Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.

### 11. The Binomial Theorem: Defining Expressions

In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.

### 12. How to Divide Polynomials with Long Division

Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!

### 13. How to Use Synthetic Division to Divide Polynomials

Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!

### 14. Dividing Polynomials with Long and Synthetic Division: Practice Problems

Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!

### 15. Operations with Polynomials in Several Variables

In this video lesson, you will learn how to handle and work with polynomials that have more than one variable. This is important because in math you sometimes have to work with several variables at the same time.

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### Other Chapters

Other chapters within the ACT Compass Math Test: Practice & Study Guide course

- Compass Math: Integers
- Compass Math: Decimals
- Compass Math: Fractions
- Compass Math: Exponents
- Compass Math: Roots & Radicals
- Compass Math: Percents
- Compass Math: Ratios, Rates & Proportions
- Compass Math: Median, Mean & Mode
- Compass Math: Algebraic Equations & Expressions
- Compass Math: Linear Equations
- Compass Math: Substituting Values
- Compass Math: Factoring Polynomials
- Compass Math: Matrices & Absolute Value
- Compass Math: Inequalities
- Compass Math: Complex Numbers
- Compass Math: Logarithms
- Compass Math: Basic Geometry
- Compass Math: Lines & Angles
- Compass Math: Polygons
- Compass Math: Triangles
- Compass Math: Quadrilaterals
- Compass Math: Circles
- Compass Math: Similar Figures
- Compass Math: Complex Figures
- Compass Math: Constructions
- Compass Math: Area, Circumference & Perimeter
- Compass Math: Mathematical Modeling
- Compass Math: Quadratics
- Compass Math: Quadratic Functions
- Compass Math: Trigonometric Functions
- Compass Math: Rational Functions
- Compass Math: Function Operations
- Compass Math: Trigonometric Identities
- Compass Math: Trigonometric Equations
- Compass Math: Trigonometric Applications
- Compass Math: Trigonometric Graphs
- Compass Math: Graph Symmetry
- Compass Math: Polar Coordinates & Parameterization