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