Appendix C - Synthetic Division and the Remainder Theorem - C Exercise Set - Page 993: 18

$y^4+y^3+y^2+y+1$

Equating the divisor to zero of the given expression, $( y^5-1 )\div( y-1 ),$ and then solving for the variable, then \begin{align*} y-1&=0 \\ y&=1 .\end{align*} Using $ 1 $ in manipulating the coefficients of the dividend results to the picture shown below. The last row of numbers, $\{ 1,1,1,1,1,0 \},$ represent the coefficients of the quotient and the remainder. Hence, $( y^5-1 )\div( y-1 )$ is equal to \begin{align*} y^4+y^3+y^2+y+1 .\end{align*}