Answer
Doesn't make sense.
Work Step by Step
Doesn't make sense, because the division of $x^5+1$ by $x+1$ is,
$\begin{array}{lllllll}
& & x^{4} & -x^{3} & +x^2 & -x & +1 \\
& -- & -- & -- & -- & -- & \\
x+1\ ) & x^{5} & +0x^{3} & +0x^{2} & +0x & +1 & \\
& -x^{5} & -x^{4} & & & & \\
& -- & -- & & & & \\
& & -x^4 & +0 & & & \\
& & x^{4} & +x^{3} & & & \\
& & -- & -- & & & \\
& & & x^{3} & +0 & & \\
& & & -x^{3} & -x^2 & & \\
& & & -- & -- & & \\
& & & & -x^2 & +0 & \\
& & & & x^2 & +x & \\
& & & & -- & -- & \\
& & & & & x &+1 \\
& & & & & -x &-1 \\
& & & & & -- & -- \\
& & & & & & 0
\end{array}$
$q(x)=x^{4}-x^{3}+x^2 -x+1$
$r(x)=0$
We can see that the quotient of dividing $x^5+1$ by $x+1$ is not equal to the answer we guessed just by looking at the equation of $x^4+1$. Therefore, It is important to follow all the step in doing long division as seen above to get the correct answer.
