Übung
$\frac{2x^4-x^3+x^2-10}{x-3}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $2x^4-x^3+x^2-10$ durch $x-3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}2x^{3}+5x^{2}+16x\phantom{;}+48\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}2x^{4}-x^{3}+x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-2x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+6x^{3};}\phantom{;}5x^{3}+x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-5x^{3}+15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{3}+15x^{2}-;x^n;}\phantom{;}16x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-16x^{2}+48x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-16x^{2}+48x\phantom{;}-;x^n-;x^n;}\phantom{;}48x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-48x\phantom{;}+144\phantom{;}\phantom{;}}\\\phantom{;;;-48x\phantom{;}+144\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}134\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}+5x^{2}+16x+48+\frac{134}{x-3}$
Endgültige Antwort auf das Problem
$2x^{3}+5x^{2}+16x+48+\frac{134}{x-3}$