Digital PSAT Math Practice Question 174: Answer and Explanation

Question: 174

What are the values of a in this equation?

3a² - 27a - 108 = 0

• A. -9, -3
• B. 6, -4
• C. 9, 6
• D. 12, -3

Correct Answer: D

Explanation:

(D) You could work backwards from the choices if you are so inclined. Algebraically, divide the expression by 3 to simplify:

Factor it: (a - 12)(a + 3) = 0

If a = 12, (a - 12) is 0, making the entire expression equal to 0. Similarly, if a = -3, (a + 3) is 0, making the entire expression equal to 0.

Therefore, the solutions are 12, -3.