Which polynomial is prime? 3x^3+3x^2-2x-2 3x^3-2x^2+3x-4 4x^3+2x^2+6x+3 is 4x^3+4x^2-3x-3

To determine which polynomial is prime, we need to check if any of the given polynomials can be factored into the product of two or more non-constant polynomials with coefficients in the field of real numbers.<br /><br />Let's analyze each polynomial one by one:<br /><br />1. $3x^{3}+3x^{2}-2x-2$:<br /> This polynomial can be factored as $(x+1)(3x^{2}-2)$, so it is not prime.<br /><br />2. $3x^{3}-2x^{2}+3x-4$:<br /> This polynomial cannot be factored further, so it is prime.<br /><br />3. $4x^{3}+2x^{2}+6x+3$:<br /> This polynomial can be factored as $(x+1)(4x^{2}+2x+3)$, so it is not prime.<br /><br />4. $4x^{3}+4x^{2}-3x-3$:<br /> This polynomial can be factored as $(x-1)(4x^{2}+4x+3)$, so it is not prime.<br /><br />Therefore, the polynomial that is prime is $3x^{3}-2x^{2}+3x-4$.