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.
- 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
- 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
- The correct answer is Choice (C).
Product means “multiply.” This is a simple FOIL operation:
(x + 2)(x – 5) = x2 – 3x –10
- 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.