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

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

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add a pic of the graph, then ill edit this "answer" and solve it for you : 3

step-by-step explanation: