Determine if x + 3 is a factor of - 3x^3+6x^2+6x+9, and how do you know?

Begin by taking out - 3 as a common factor.

-3 (x^3 - 2x^2 - 2x - 3)

If x + 3 is a factor, what is inside the brackets should be 0 when x = - 3 It is not. There is only one real root and that is when (x - 3) is equated to 0. Just to show the root is + 3, the graph is included.