real and imaginary solutions

Question

Find all real and imaginary solutions to the equation n^3-8n^2-nt8=0 

Answer 1

It appears that the expression nt8 just before the equals sign should be  n+8.  

With that the equation reads:

     n³ - 8n² -n + 8 =0.

 

The factor by grouping approach works.   Rewrite as

 

   n² (n -8)  - (n -8)  =0       the (n-8) is a common factor so

 

     (n² -1) (n-8)  = 0   and

      (n + 1) (n -1) (n-8)  =0.

 

  So the solutions are all real.

  The solution set is   {-1, 1, 8}