Ch 19: GRE Quantitative Reasoning: Factoring with FOIL, Graphing Parabolas and Solving Quadratics

About This Chapter

Review elements of factoring and solving quadratics to prepare for the Graduate Record Exam (GRE). Video lessons and quizzes incorporate elements of the quantitative reasoning section in a simple and clear manner.

GRE Quantitative Reasoning: Factoring with FOIL, Graphing Parabolas and Solving Quadratics - Chapter Summary

Improve your understanding of quadratic equations and methods of solving them with our GRE training lessons. Videos cover algebraic concepts found on the quantitative reasoning part of the GRE. Lessons specifically address subjects such as:

  • Binomials
  • The FOIL method
  • The area method
  • Quadratic equations
  • Completing the square
  • Parabolas

In addition to offering instruction in these areas, the lectures in this chapter include corresponding quizzes and, in some cases, practice problems to let you gauge your comprehension of the material. Each subject is broken down into a short video lesson to help you grasp the concepts and score well on the GRE.

GRE Quantitative Reasoning Objectives

The GRE is used to evaluate students' capacity to undertake graduate-level study. The test's quantitative reasoning section accounts for approximately one-third of the total exam. Our factoring and quadratics lessons address areas covered in this segment of the actual GRE. Some particular topics addressed are:

  • Using the FOIL (firsts, outsides, insides, lasts) method to multiply binomials
  • Multiplying binomials with the area method
  • Understanding the quadratic formula
  • Employing factoring to solve quadratic equations
  • Transitioning non-standard quadratic equations into standard form
  • Identifying different types of parabolas
  • Understanding how to transfer a standard-form quadratic equation into vertex form (i.e., complete the square)

The GRE's quantitative reasoning component incorporates both multiple-choice questions and problems that ask you to calculate and enter a numeric answer. Subjects covered include data analysis, geometry, algebra, and arithmetic.

11 Lessons in Chapter 19: GRE Quantitative Reasoning: Factoring with FOIL, Graphing Parabolas and Solving Quadratics
Test your knowledge with a 30-question chapter practice test
What is a Parabola?

1. What is a Parabola?

A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.

Parabolas in Standard, Intercept, and Vertex Form

2. Parabolas in Standard, Intercept, and Vertex Form

By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.

Multiplying Binomials Using FOIL and the Area Method

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.

Multiplying Binomials Using FOIL & the Area Method: Practice Problems

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.

How to Use the Quadratic Formula to Solve a Quadratic Equation

5. 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.

How to Factor Quadratic Equations: FOIL in Reverse

6. 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.

How to Solve a Quadratic Equation by Factoring

7. 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!

Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient

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!

How to Complete the Square

9. 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.

Completing the Square Practice Problems

10. 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!

How to Solve Quadratics That Are Not in Standard Form

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support