# Ch 6: Solving Problems with Polynomials

### About This Chapter

## Solving Problems with Polynomials - Chapter Summary

In this interesting chapter, you'll review problem solving with polynomials. Our short lessons define polynomials, binomials and quadratics, and explain how to perform basic operations like addition, subtraction and multiplication with them. The chapter also details solving quadratics that are not in standard form. After completing this chapter, you should be ready to:

- Define special product and the formula used to find it
- Use the rational zeros theorem to find rational zeros
- Outline the steps needed to use quadratic form to factor polynomials
- Explain polynomial identities
- Give an example of a quadratic equation
- Add and subtract rational expressions in practice questions

Even the most challenging topics are easy with these professionally designed and self-paced learning tools. Each lesson is followed by a short quiz, so you can test your knowledge before moving on to other topics. If you'd like to review just one topic in a video lesson, use the video tags feature to skip ahead. Feel free to reach out to an instructor if any of the material is confusing.

### 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. Special Product: Definition & Formula

In this lesson, we will review what a binomial is and how to multiply two binomials together. We will then discuss special cases called special products.

### 4. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.

### 5. 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.

### 6. What Are Polynomial Identities?

Polynomial identities are effective tools for making our work with polynomials much easier. In this lesson, we will define polynomial identities and explore some useful examples.

### 7. What is a Quadratic Equation? - Definition & Examples

You might be surprised to learn that quadratic equations are an important part of the world we live in. We sometimes even make use of them for our entertainment! Watch this video lesson to learn more about these equations.

### 8. How to Factor Quadratic Equations: FOIL in Reverse

So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1.

### 9. 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.

### 10. How to Solve Quadratics That Are Not in Standard Form

It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form.

### 11. How to Add and Subtract Rational Expressions

Adding and subtracting rational expressions brings everything you learned about fractions into the world of algebra. We will mix common denominators with factoring and FOILing.

### 12. Practice Adding and Subtracting Rational Expressions

Adding and subtracting rational expressions can feel daunting, especially when trying to find a common denominator. Let me show you the process I like to use. I think it will make adding and subtracting rational expressions more enjoyable!

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### Other Chapters

Other chapters within the Pennsylvania Algebra I Keystone Exam: Test Prep & Practice course

- Real Numbers & Expressions
- Understanding Exponential Expressions
- Working with Radical Expressions
- Understanding Absolute Value Expressions
- Estimation & Math Problem-Solving
- Solving, Writing & Graphing Linear Equations
- Solving Problems with Systems of Equations
- Solving & Graphing Linear Inequalities
- Understanding Function Basics
- Using Scatter Plots
- Understanding Basic Statistics
- Interpreting & Graphing Data
- Understanding the Probability of Compound Events
- Pennsylvania Algebra I Keystone Exam Flashcards