Question 141202
First, note that the statement is the same as:

f(x)=x^3+3^3=(x+3)(x^2-3x+9) by the formula for the sum of cubes.

Attempting to find the zeros, we set f(x)=0:
(x+3)(x^2-3x+9)=0

This can only be when
x=-3  or x^2-3x+9=0
We can see that the second will not have any real roots because the discriminant is negative b^2-4ac=9-4(1)(9)=-27. 
Thus, your choice of b is correct, but I would recommend using the method I have done here to determine the amount of roots of a polynomial.