How to use synthetic division to find all zeros of f?

Question

So the full question is use synthetic division to divide f(x) = x³ - 2x² - 13x - 10 by x + 2.  Use the result to find all zeros of f.  I don't understand how to do this at all and I have a final tomorrow so it's kinda important I learn.

Answer 1

                X^2 -4x -5                               

   X + 2 l X^3 - 2X^2 - 13X - 10

              X^3  ± 2X^2                    

                       -4X^2 -13X

                       - 4X^2 -8X

                       +        +        

                                 -5X -10

                                 - 5X-10 

                                      0

 

       Then:

       X^3 - 2X^2 - 13X - 10 = ( X +2 ) ( X^2 - 4X - 5 )