SAT Math

Answer: C - Two numbers can be substituted in the expression so that the result is a prime number.
(n^4 + n^3-n-1)/3 = (n^3 (n + 1)-(n + 1))/3 = (n + 1)(n^3-1)/3 = (n + 1)(n-1)(n^2 + n + 1)/3 =
= (n^2-1)(n^2 + n + 1)/3
n^2 + n + 1 can’t be factorized.
n^2-1 = 3
n^2 = 4
n = ±2
For n = ±2, the expression (n^2-1)(n^2 + n + 1)/3 transforms into n^2 + n + 1, which is a prime number. Therefore, there are two numbers for which the expression (n^4 + n^3-n-1)/3 is a prime number.