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