SAT Prep

Answer: C - Two numbers can be substituted in the expression so that the result is a prime number.
(n⁴ + n³-n-1)/3 = (n³ (n + 1)-(n + 1))/3 = (n + 1)(n³-1)/3 = (n + 1)(n-1)(n² + n + 1)/3 =
= (n²-1)(n² + n + 1)/3
n² + n + 1 can’t be factorized.
n²-1 = 3
n² = 4
n = ±2
For n = ±2, the expression (n²-1)(n² + n + 1)/3 transforms into n² + n + 1, which is a prime number. Therefore, there are two numbers for which the expression (n⁴ + n³-n-1)/3 is a prime number.