For how many different positive integers n is a divisor of n^3 + 8?
The question asks for how many different positive integers n, n^3+8 is divisible by n.
Well the first term n^3 is divisible by n, the second term, 8, to be divisible by n, should be a factor of 8.
8=2^3 hence it has 3+1=4 factors: 1, 2, 4, and 8. Therefore n^3+8 is divisible by n for 4 values of n: 1, 2, 4, and 8.
Bunnel at first I got the answer 4.
Then I plugged in n=3 and got zero. PS questions are supposed to have one right answer. Why are we using only 2