Complex_P

 I know, from computing experience, that the cube root of 27 is 3.

or again, 3, -3, -3. I can test for truth by multiplying these roots and

getting back to 27. 

But invoking the complex plane will produce results that may seem puzzling:

                                                  

                                                                               

On the complex plane, these other roots also verify 27. That is de Moivre's theorem, 1707.

As for the cube root of -27, I know that -3 is one such root. On the complex plane:

                                                                         

                                                                    

                                                                                 

Each of the three cited roots is a root in itself.

                                                                        

source: Math is Fun

Long story short, -3 might be a factor to 27 but it is not a cubic root. In the

same vein, 3 can be a factor to -27, but cannot be considered a cube root...👩‍🦰