We have to put in a placeholder of 

÷

Since synthetic division can only be used to divide 
by expressions in the form x - A, we have to make two
divisions:

1. First we factor 3 out of  and get 
2. So we divide first synthetically by  
3. Then  we divide by 3.

Dividing first by 

-2/3| 2    -3     0      2      -5
    |     -4/3  26/9  -52/27   -4/81    
      2  -13/3  26/9    2/27  -409/81


That gives 

      

First we'll simplify that fraction on the end:

Multiply top and bottom by 81:



So dividing by  gives:

      

Now we must divide every term by 3, which is the same
as multiplying by :

      

What a terrible problem!  Are you sure you didn't copy something
wrong?

Edwin