Do it the same way as you do any synthetic division.
You just have to spread it out more so thet there is
room for the square roots, and you will have to do
some of the multiplications out to the side or on
scratch paper.

 8-Ö6|1  -8     -70       464
     |    8-Ö6    6-8Ö6  -464
      1    -Ö6  -64-8Ö6     0

We got a zero remainder, so that means that 
is a solution.

That means we have factored  



as



Now since all the coefficients are integers, the conjugate of 
that,  is also a solution.  So we do another
synthetic division using the second parentheses and the
conjugate :



   8+Ö6|1   -Ö6  -64-8Ö6
       |   8+Ö6   64+8Ö6
        1  8           0  

Now we have finally factored the polynomial this way:



Set those three factors equal to 0 and you get the three
solutions:

, , 

Edwin