Which polynomial is prime x^3+3x^2+2x+6

Step-by-step explanation:

Prime numbers have only one factor pair, the number itself and 1. Some polynomials can be factored and some cannot be so a polynomial is a prime polynomial if it can't be factored into the standard linear form of (x+a) ((x+b).

For the given polynomial x^3+3x^2+2x+6

Re-arranging the Polynomial to find out whether it could be factored or not

x^3+2x+3x^2+6=0

x (x^2+2) + 3 (x^2+2) = 0

(x+3) (x^2+2) = 0

x+3=0 and x^2+2=0

x=-3, x^2 = - 2

x=-3, x=sqrt (-2), x = - sqrt (-2)

As the polynomial is factorable it is not prime