PSAT Math Grid-Ins Question 32: Answer and Explanation

Question: 32

8y² - dy - 15

If 2y - 3 is a factor of the expression above, in which d is an integer, what is the value of d?

Correct Answer: 2

Explanation:

2

The question asks for the value of one of the coefficients in a quadratic. When given a quadratic in standard form, which is ax² + bx + c, it is often necessary to factor it to solve the question. Here, the question supplies one of the factors, so use that to find the other factor. If (2y - 3) is a factor, then the first part of the second factor must multiply by 2y to result in 8y². Divide 8y² by 2y to get 4y as the first term in the second factor. Similarly, the second term in the second factor must multiply by -3 to get -15. Divide -15 by -3 to get 5 as the second term of the second factor. Therefore, the second factor must be (4y + 5). Now use FOIL on the two factors to both verify that these numbers give you 8y² and -15 and to determine the coefficient on the y term, which will be the value of d. The expression becomes (2y - 3)(4y + 5) = 8y² + 10y - 12y - 15 or 8y² - 2y - 15. Therefore, d = 2. The correct answer is 2.