About This Chapter
How It Works:
- Identify the lessons in the Big Ideas Math Polynomial Equations & Factoring chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the information about polynomial equations and factoring that you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Definitions for polynomials, binomials and quadratics
- How to subtract, add and multiply polynomials
- How to multiply binomials
- How perfect square binomials are defined
- The zero product property
- How to factor polynomial expressions
- The difference of two squares theorem
- How to factor quadratic equations
- How to factor polynomials using quadratic form
Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.
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 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.
4. Binomials: Difference of Two Squares
Sometimes a difficult calculation can be simplified and a complicated math expression can be made smaller with factoring formulas. In this lesson we explore one of the factoring formulas called the difference of squares.
5. 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.
6. Zero Product Property: Definition & Examples
After completing this lesson, you will be able to state the Zero Product Property and apply it to real numbers and algebraic expressions. You will also be able to solve equations using the Zero Product Property.
7. 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.
8. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here!
9. How to Use the Difference of Two Squares Theorem to Solve Quadratic Equations
When a quadratic formula is made up of the difference between two perfect squares, factoring becomes much easier. In this lesson we'll explore how to use the Difference Between Two Squares Theorem to solve certain quadratic equations.
10. Factoring Polynomials Using Quadratic Form: Steps, Rules & Examples
Factoring a polynomial of degree 4 or higher can be a difficult task. However, some polynomials of higher degree can be written in quadratic form, and the techniques used to factor quadratic functions can be utilized.
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Other chapters within the Big Ideas Math Algebra 1: Online Textbook Help course
- Big Ideas Math Algebra 1 - Chapter 1: Solving Linear Equations
- Big Ideas Math Algebra 1 - Chapter 2: Solving Linear Inequalities
- Big Ideas Math Algebra 1 - Chapter 3: Graphing Linear Functions
- Big Ideas Math Algebra 1 - Chapter 4: Writing Linear Functions
- Big Ideas Math Algebra 1 - Chapter 5: Solving Systems of Linear Equations
- Big Ideas Math Algebra 1 - Chapter 6: Exponential Functions & Sequences
- Big Ideas Math Algebra 1 - Chapter 8: Graphing Quadratic Functions
- Big Ideas Math Algebra 1 - Chapter 9: Solving Quadratic Equations
- Big Ideas Math Algebra 1 - Chapter 10: Radical Functions & Equations
- Big Ideas Math Algebra 1 - Chapter 11: Data Analysis & Displays