Answer:\(3x^3-2x^2+3x-4\)
Step-by-step explanation:
We know that a polynomial is said to be prime if it does not factorize into polynomials.
1. \(3x^3+3x^2-2x-2\\=3x^2(x+1)-1(x+1)\\=(x+1)(3x^2-1)\)
This is not prime as it can factorize.
2.\(3x^3-2x^2+3x-4\\=x^2(3x-2)+1(3x-4)\)
\((3x-2)\ and\ (3x-4)\) are not same , thus we cannot factorize the above polynomial.
Therefore this polynomial is prime.
3.\(4x^3+2x^2+6^x+3=2x^2(2x+1)+3(2x+1)\\=(2x+1)(2x^2+3)\)
This is not prime as it can factorize.
4.\(4x^3+4x^2-3x-3\\=4x^2(x+1)-3(x+1)\\=(x+1)(4x^2-3)\)
This is not prime as it can factorize.
