SAT Practice Math Questions—FOIL Operations

The SAT Math exam will throw some questions at you where you’ll be expected to know how to perform a FOIL operation—where you multiply a polynomial in the order, First, Outer, Inner, and Last.

The following practice questions ask you to find the product of two binomials and the value of a variable using the FOIL method.

Practice questions

1. Which of the following is the product of these two binomials? x + 2 x – 5 A. x² – 10 B. x² + 10 C. x² – 3x – 10 D. x² + 3x – 10
2. If x – 2 is a factor of x² + 6x – y² and y > 0, what is the value of y? Note: this would be a grid-in question. Because there are no multiple-choice answers, you need to supply the correct answer.

Answers and explanations

1. The correct answer is Choice (C). Product means "multiply." This is a simple FOIL operation: (x + 2)(x – 5) = x² – 3x –10
2. The correct answer is 4. If x – 2 is a factor of the polynomial, then for the middle part of the polynomial to be 6x, the other factor must be (x + 8). Write out these factors and FOIL the expression: (x – 2)(x + 8) = (x² + 6x – 16) The given polynomial is x² + 6x – y², so this means that y² = 16, and because y is positive, it must equal 4.