Question 789685
Excuse me for handling your question like this:
but, did you mean, "polynomial division", or did you mean as you said, synthetic division?  Either way, the process will be messy.  


To use regular polynomial division, you would use {{{x^4+0x^3+0x^2+0x-16}}} as dividend, and {{{x-1+sqrt(2)}}} as divisor.