1. The problem statement, all variables and given/known data We have a polynomial of fourth degree. I want to use synthetic division. However, is synthetic division applicable at all times? Are there cases in which the first binome extracted cannot have an integrer? What do I do at that time? 2. Relevant equations Synthetic division. 3. The attempt at a solution I have absolutely no clue which other method to use. I searched on purplemath and other websites, but can't find an example where the polynomials are fractions. I'm lost and I've been working on this for hours :P I'll take a break before reading your valuable answers. Thanks in advance.