which polynomial is prime? (x4 + 3x2 – x2 – 3)(x4 – 3x2 – x2 + 3)(3x2 + x – 6x – 2)(3x2 + x – 6x + 3)

A polynomial is prime when it can't be factored anymore:
For
x4 + 3x2 – x2 – 3
It can still be factored into:
(x2 - 1)(x2 + 3)

For
x4 – 3x2 – x2 + 3
It can still be factored into:
(x2 - 3)(x2 -1)

For
3x2 + x – 6x – 2
It can still be factored into:
(3x + 1)(x - 2)

For
3x2 + x – 6x +3
It can't be factored anymore using real number.

Therefore, the last option is the prime polynomial

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