Übung
$\frac{x^8-1}{x^5+x^3+x+2}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $x^8-1$ durch $x^5+x^3+x+2$
$\begin{array}{l}\phantom{\phantom{;}x^{5}+x^{3}+x\phantom{;}+2;}{\phantom{;}x^{3}\phantom{-;x^n}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{5}+x^{3}+x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{5}+x^{3}+x\phantom{;}+2;}\underline{-x^{8}\phantom{-;x^n}-x^{6}\phantom{-;x^n}-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{8}-x^{6}-x^{4}-2x^{3};}-x^{6}\phantom{-;x^n}-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{5}+x^{3}+x\phantom{;}+2-;x^n;}\underline{\phantom{;}x^{6}\phantom{-;x^n}+x^{4}\phantom{-;x^n}+x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{6}+x^{4}+x^{2}+2x\phantom{;}-;x^n;}-2x^{3}+x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-x+\frac{-2x^{3}+x^{2}+2x-1}{x^5+x^3+x+2}$
Endgültige Antwort auf das Problem
$x^{3}-x+\frac{-2x^{3}+x^{2}+2x-1}{x^5+x^3+x+2}$