PLEASE HELP!!!!

Question

Write an example of a cubic polynomial that is prime and then explain how you know it is prime. Your polynomial cannot be a monomial. Write your answer as a sentence.

Answer 1

P(x) = x^3 + 2

P = {+-1, +-2}

Q = {+-1}

the only possible rational solutions are P/Q = {+-1, +-2}

P(1) = 3

P(-1) = 1

P(2) = 10

P(-2) = -6

there are no rational solutions, so it cannot be factored...

therefore it is prime