`( x+ 1)(x^4 - x^3 + x^2 -x +1)`
`= x.x^4 - x.x^3 + x.x^2 -x.x + x.1 + 1.x^4 - 1.x^3 + 1.x^2 - 1.x +1.1`
`= x^5 - x^4 + x^3 - x^2 + x +x^4 - x^3 + x^2 -x+2`
`= x^5 + (-x^4 + x^4) + (x^3 -x^3) + (-x^2 + x^2) +(x-x) +1`
`= x^5 + 0 + 0 + 0 + 0 + 1`
`= x^5 + 1`
$#Dyn.Shun$
$@Shun$~