Which polynomial is prime?

A. x4 + 3x2 - x2 - 3

B. x4 - 3x2 - x2 + 3

C. 3x2 + x - 6x - 2

D. 3x2 + x - 6x + 3

A polynomial is prime if it can not be factored or (what is equivalent) it cannot be divided (leaving residue = 0).

A) can be factored as x^2 (x^2+3) - (x^2 + 3) = (x^2+3) (x^2-1)

B) can be factored as x^2 (x^2 - 3) + (x^2 - 3) = (x^2 - 3) (x^2 + 1)

C) can be factored as x (3x + 1) - 2 (3x + 1) = (3x + 1) (x - 2)

D) cannot be divided without leaving a residue, so the answer is option D.