# Ch 9: Algebra - Polynomials: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other GMAT prep work.
- Identify the polynomials concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our GMAT prep tutoring solution will benefit any student who is trying to learn polynomials and prepare for the exam. This resource can help students including those who:

- Struggle with understanding how to add or subtract polynomials, use FOIL, divide polynomials, factor quadratic equations, complete the square, use the quadratic formula or any other polynomials topic
- Have limited time for studying
- Want a cost effective way to supplement their algebra learning
- Prefer learning algebra skills visually
- Find themselves struggling to prepare for the GMAT
- Cope with ADD or ADHD
- Want to get ahead in preparing for the GMAT
- Don't have access to their GMAT prep instructor outside of class

## Why it works:

**Engaging Tutors:**We make learning polynomials simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live GMAT tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn polynomials on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning objectives:

- Define quadratics, polynomials and binomials.
- Use the FOIL and area methods to multiply binomials.
- Add, subtract and multiply polynomials.
- Use synthetic and long division to divide polynomials.
- Solve non-standard form quadratics.
- Learn how to complete the square.
- Complete practice problems.
- Factor quadratic equations using the FOIL in reverse technique.
- Use quadratic formulas to solve quadratic equations and equations with literal coefficients.

### 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. Multiplying Binomials Using FOIL & the Area Method: Practice Problems

There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials.

### 5. 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.

### 6. 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!

### 7. 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!

### 8. 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!

### 9. 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!

### 10. How to Solve a Quadratic Equation by Factoring

If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video!

### 11. 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.

### 12. How to Complete the Square

Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.

### 13. Completing the Square Practice Problems

Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!

### 14. How to Use the Quadratic Formula to Solve a Quadratic Equation

When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson.

### 15. Using the Quadratic Formula to Solve Equations with Literal Coefficients

Watch this video lesson to find out what steps you need to take to solve equations with literal coefficients using the quadratic formula. Learn why it might be easier to work with literal coefficients than with number coefficients.

### 16. Solving Problems using the Quadratic Formula

The quadratic formula is not as complicated as it may look. You can learn to tackle this formula and succeed in using it to help you solve your quadratic problems. Watch this video to see how.

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### Other Chapters

Other chapters within the GMAT Prep: Tutoring Solution course

- Basic Arithmetic Calculations: Tutoring Solution
- Rational Numbers: Tutoring Solution
- Decimals and Percents: Tutoring Solution
- Data & Statistics: Tutoring Solution
- Basic Algebraic Expressions: Tutoring Solution
- Exponents: Tutoring Solution
- Algebraic Linear Equations & Inequalities: Tutoring Solution
- Algebra - Absolute Value Equations & Inequalities: Tutoring Solution
- Algebra - Rational Expressions: Tutoring Solution
- Perimeter, Area & Volume: Tutoring Solution
- Geometric Properties of Objects: Tutoring Solution
- Geometric Graphing Basics: Tutoring Solution
- Geometric Graphing Functions: Tutoring Solution
- Conventions in Writing - Grammar: Tutoring Solution
- Usage Conventions in Writing: Tutoring Solution
- Reading Comprehension for Test-Taking: Tutoring Solution
- Critical Reasoning for Test-Taking: Tutoring Solution
- Practical Applications for Test-Taking: Tutoring Solution
- Essay Writing Basics: Tutoring Solution
- Essay Clarity: Tutoring Solution
- Editing Your Writing: Tutoring Solution
- Practicing Analytical Writing: Tutoring Solution