SAT Practice Math Questions—FOIL Operations

By Ron Woldoff

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 + 6xy2 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 + 6xy2, so this means that y2 = 16, and because y is positive, it must equal 4.