Übung
$\frac{2x^4-3x^2+5x-1}{x+5}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $2x^4-3x^2+5x-1$ durch $x+5$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}2x^{3}-10x^{2}+47x\phantom{;}-230\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}2x^{4}\phantom{-;x^n}-3x^{2}+5x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-2x^{4}-10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-10x^{3};}-10x^{3}-3x^{2}+5x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}10x^{3}+50x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}10x^{3}+50x^{2}-;x^n;}\phantom{;}47x^{2}+5x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-47x^{2}-235x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-47x^{2}-235x\phantom{;}-;x^n-;x^n;}-230x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}230x\phantom{;}+1150\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}230x\phantom{;}+1150\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}1149\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}-10x^{2}+47x-230+\frac{1149}{x+5}$
Endgültige Antwort auf das Problem
$2x^{3}-10x^{2}+47x-230+\frac{1149}{x+5}$