2024 AMC 8 Problems/Problem 22
Problem 22
What is the sum of the cubes of the solutions cubed of ?
(A) 1 (B) 8 (C) 27 (D) -1 (E) -27
Solution
Factoring yields . Denote to be solutions of this polynomial. We can easily find one of the solutions is . Using the quadratic formula on the rest of the factors yields and finally . The sum is 1, so 1 to the third power is 1. So, the final answer is .
-Rainier2020
Sidenote: You also could have used Newtonian sums to solve this problem.