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