Question 127646
You do this by long division. The only way to learn it
is to know the rules and practice. If you don't have
a good explanation in your textbook, I would google
"division polynomials" and take your pick.
The answer to your problem is {{{x^4 - x^3 + x^2 - x + 1}}}
Multiply it by {{{x + 1}}} and you should get {{{x^5 + 1}}}