What are the zeros of the polynomial function?

$\begin{align} f(x)&=x^3+x^2-9x-9\\ f(x)&=x^2(x+1)-9(x+1)\\ f(x)&=(x^2-9)(x+1)\\ f(x)&=(x+3)(x+1)(x-3)\\ \end{align}\\ \therefore \text{-3, -1 and 3 are zeros of the polynomial.}$

(x^3  + x^2  - 9x  - 9) : (x + 1)  =  x^2 - 9  
 x^3  + x^2           
 ———————
             - 9x  - 9
             - 9x  - 9
             ————
                     0

x^2 - 9 = (x + 3) (x - 3)

x = -1

x = -3

x = 3