About This Chapter
Working with Polynomials - Chapter Summary
Utilize the video and text lessons in this chapter to make working with polynomials easy. Lessons explore ways to perform mathematical operations on monomials, binomials and trinomials under various circumstances. Also, learn about FOIL and the area method. Upon completion of this chapter, you will have the ability to:
- Define polynomials, binomials and quadratics
- Add, subtract, multiply and divide polynomials
- Multiply a binomial by a monomial and by using FOIL and the area method
- Show how to divide a polynomial by a monomial
- Divide polynomials with long division and synthetic division
- Perform operations with polynomials in several variables
- Demonstrate how to factor polynomial expressions
- Show your understanding of the perfect square binomial and trinomial
Feel confident that you understand all that is required in working with polynomials by reviewing the lessons at your leisure. Access them any time, day or night, and revisit them as often as needed. If you want help understanding a lesson concept, feel free to submit your questions to our experts. When ready, test your knowledge of polynomials by taking lesson quizzes and a chapter exam.
1. What are Polynomials, Binomials, and Quadratics?
What do polynomials, binomials, and quadratics have in common? What are their differences? How can you identify each of them? Watch this video lesson to find the answers.
2. 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!
3. Multiplying a Binomial by a Monomial
To multiply mathematical expressions with only one term (monomials) and mathematical expressions with two terms (binomials), you can use the distributive property of algebra. In this lesson, you will learn how it works.
4. Multiplying Binomials Using FOIL and the Area Method
From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.
5. Dividing a Polynomial by a Monomial
In this lesson, learn about polynomials and monomials and the 3 simple steps you can use to divide a polynomial by a monomial. Then, you will get a chance to practice it yourself!
6. 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!
7. 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!
8. 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.
9. Factoring Polynomial Expressions
When it comes to factoring polynomials, there are several methods to choose from depending on what kind of polynomial you are looking at. Watch this video lesson to learn how to identify and use the appropriate method.
10. Perfect Square Binomial: Definition & Explanation
Learn what sets perfect square binomials apart from other trinomials in the math world. You will also learn an easy method to identify them along with a simple procedure to factor them.
11. Perfect Square Trinomial: Definition, Formula & Examples
Perfect square trinomials are a special group of polynomials that can be factored into a very convenient pattern, making them very useful in solving equations.
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Other chapters within the STAAR Algebra I: Test Prep & Practice course
- Arithmetic & Geometric Sequences
- Understanding Square Roots
- Exponential Expression Math
- Basics of Solving Word Problems
- Understanding Coordinate Graphs
- Understanding Linear Equations
- The Basics of Functions
- Graphing Linear Functions & Equations
- Exponential Functions
- Calculating & Graphing Inequalities
- Algebraic Distribution
- Overview of Algebraic Expressions
- Overview of Algebraic Equations
- Solving Quadratic Equations
- Using a Graphing Calculator
- About the STARR Tests
- STAAR Algebra I Flashcards