Übung
$\frac{\left(2x^4+x^3+15x^2+18x-27\right)}{\left(x-1\right)}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $2x^4+x^3+15x^2+18x-27$ durch $x-1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}2x^{3}+3x^{2}+18x\phantom{;}+36\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}2x^{4}+x^{3}+15x^{2}+18x\phantom{;}-27\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-2x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+2x^{3};}\phantom{;}3x^{3}+15x^{2}+18x\phantom{;}-27\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-3x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}+3x^{2}-;x^n;}\phantom{;}18x^{2}+18x\phantom{;}-27\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{-18x^{2}+18x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-18x^{2}+18x\phantom{;}-;x^n-;x^n;}\phantom{;}36x\phantom{;}-27\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{-36x\phantom{;}+36\phantom{;}\phantom{;}}\\\phantom{;;;-36x\phantom{;}+36\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}9\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}+3x^{2}+18x+36+\frac{9}{x-1}$
Endgültige Antwort auf das Problem
$2x^{3}+3x^{2}+18x+36+\frac{9}{x-1}$