Find the remainder for $\dfrac{x^5-x^4+x^3+2x^2-x+4}{x^3+1}$
I know exactly how to synthetically divide in the format of: $(x\pm a)$. But not $(x^n\pm a)$ (with an exponent). So if anyone can tell me if anything changes or if the steps are the exact same just with the remainder as $\dfrac{remainder}{x^n\pm a}$. And please do not solve the problem for me.
Edit:
I think I've reached an answer. Long division confused me so I used expanded synthetic division and got: $x^2-x+1+\left(\dfrac{x^2+3}{x^3+1}\right)$. Can anyone verify my answer please.