Which polynomial is prime? x3+3x2-2x-6 x3-2x2+3x-6 4x4+4x3-2x-2 2x4+x3-x+2

A prime polynomial is a polynomial that can't be factored.In order to check which polynomial is prime, we need to check which polynomials could be factored.x^3 + 3x^2 – 2x – 6 can be factored as (x+3)(x^2-2)x^3 – 2x^2 + 3x – 6 can be factored as (x-2)(x^2+3)4x^4 + 4x^3 – 2x – 2 can be factored as 2(x+1)(2x^3-1)2x^4 + x^3 – x + 2 can't be factored.Therefore, 2x^4 + x^3 – x + 2 is a prime polynomial.