We can help you get into your dream school.

Sign up for Magoosh SAT or Magoosh ACT Prep.

Chris Lele

SAT Math Basics – FOIL Method

The SAT loves testing questions that rely on the FOIL method. A subset of algebra, FOIL relates to polynomials, and, unlike many other algebra sections, you cannot rely on plugging in (a method I otherwise encourage you to use often).

Before I tell you exactly how to use FOIL, it is important that I tell you what a polynomial is. Take a look at the equation below:

(x - y)(x + y) = 0

Remember that parentheses stand for multiplication. Multiplying x and y may seem daunting but using the FOIL method makes things easy!

Think of the position of the x’s and the y’s above. The first position in each parenthesis consists of x’s. The last position consists of y’s.’ Using this logic, let’s apply the FOIL method:

F: First , x^2

O : Outer, xy

I : Inner, -xy

L : Last, -y^2

Now think of the variables above as part of a large addition problem:

x^2 + xy - xy - y^2 = 0

x^2 - y^2 = 0.

Practice FOIL-ing!

(x + 2)(x - 4) = 0

F: x^2

O: -4x

I: 2x

L: -8

x^2 - 2x - 8 = 0

You can also reverse the direction in which you do FOIL. For instance:

x^2 - 4x + 4 = 0

First , set up the parentheses.

(x - ?)(x - ?) = 0

The question marks are in the last position. When we multiply them together we get 4 (notice the +4 at the end of the equation). So we know that the last numbers (the question marks), when multiplied, have to equal +4.

Now note, the -4x in the middle of the equation. The outer (x * ?) + (x * ?) = -4x. Which two numbers, when multipliedf equal +4, and when added = -4. You may have to play around with the factors a little, but since the only factors of 4 are 2, 2 and 4, 1, this problem isn’t too tough. 4 and 1 would add up to 5. Therefore, 2 and 2 are the answers, and we can replace the question marks with 2’s, giving us:

(x - 2)(x - 2) = 0

Practice Question

Which of the following is a root of the equation 2x^2 - 20x = 48?

  1. -4
  2. 2
  3. 6
  4. 8
  5. 12

Answer and Explanation:









You can also watch the video explanation here: http://sat.magoosh.com/questions/117



Using FOIL takes a little bit of practice, but if you want to do well on the SAT you should definitely understand how it works.

About Chris Lele

Chris Lele is the GRE and SAT Curriculum Manager (and vocabulary wizard) at Magoosh Online Test Prep. In his time at Magoosh, he has inspired countless students across the globe, turning what is otherwise a daunting experience into an opportunity for learning, growth, and fun. Some of his students have even gone on to get near perfect scores. Chris is also very popular on the internet. His GRE channel on YouTube has over 8 million views.

You can read Chris's awesome blog posts on the Magoosh GRE blog and High School blog!

You can follow him on Twitter and Facebook!

Leave a Reply

Magoosh blog comment policy: To create the best experience for our readers, we will approve and respond to comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! :) If your comment was not approved, it likely did not adhere to these guidelines. If you are a Premium Magoosh student and would like more personalized service, you can use the Help tab on the Magoosh dashboard. Thanks!