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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.

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    do you know long division? polynomial division is exactly the same. it might help to write $x^3 + 1$ as $x^3 + 0x^2 + 0x + 1$.2012-07-20
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    I've never learned polynomial division... I know how to use long division. But it seems a little trickier with polynomials. If you could give me a medium difficulty example that would be really helpful.2012-07-20
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    @AustinBroussard Your answer is valid.2012-07-20

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