1. The problem statement, all variables and given/known data I need to construct a splitting field of f(x)=x^4-x^3-5x+5 over Q 2. Relevant equations 3. The attempt at a solution So first I will assume r is a root and divide f(x) by (x-r). The quotient came out to be x^3 + (r-1)x^2 + (r^2-r)x + r^3 - r^2 - 5. I am a bit confused what to do now, do i assume another root, call it m perhaps, and do the division again?