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.