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

A polynomial is said to be a prime if it cannot be factored. i. e. if its only factor is itself and 1. 3x^3 + 3x^2 - 2x - 2 = 3x^2 (x + 1) - 2 (x + 1) = (3x^2 - 2) (x + 1). Thus 3x^3 + 3x^2 - 2x - 2 can be factored and hence is not a prime. 3x^3 - 2x^2 + 3x - 4 cannot be further factored and hence is a prime. 4x^3 + 2x^2 + 6x + 3 = 2x^2 (2x + 1) + 3 (2x + 1) = (2x^2 + 3) (2x + 1). Thus 4x^3 + 2x^2 + 6x + 3 can be factored and hence is not a prime. 4x^3 + 4x^2 - 3x - 3 = 4x^2 (x + 1) - 3 (x + 1) = (4x^2 - 3) (x + 1). Thus 4x^3 + 4x^2 - 3x - 3 can be factored and hence is not a prime. Therefore, the polynomia that is a prime is 3x^3 - 2x^2 + 3x - 4