Übung
$\frac{2x^5+16x^4-9x^3-18x^2+9x-9}{2x^2-3}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $2x^5+16x^4-9x^3-18x^2+9x-9$ durch $2x^2-3$
$\begin{array}{l}\phantom{\phantom{;}2x^{2}-3;}{\phantom{;}x^{3}+8x^{2}-3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}2x^{2}-3\overline{\smash{)}\phantom{;}2x^{5}+16x^{4}-9x^{3}-18x^{2}+9x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{2}-3;}\underline{-2x^{5}\phantom{-;x^n}+3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{5}+3x^{3};}\phantom{;}16x^{4}-6x^{3}-18x^{2}+9x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-3-;x^n;}\underline{-16x^{4}\phantom{-;x^n}+24x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-16x^{4}+24x^{2}-;x^n;}-6x^{3}+6x^{2}+9x\phantom{;}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-3-;x^n-;x^n;}\underline{\phantom{;}6x^{3}\phantom{-;x^n}-9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6x^{3}-9x\phantom{;}-;x^n-;x^n;}\phantom{;}6x^{2}\phantom{-;x^n}-9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{2}-3-;x^n-;x^n-;x^n;}\underline{-6x^{2}\phantom{-;x^n}+9\phantom{;}\phantom{;}}\\\phantom{;;;-6x^{2}+9\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\\\end{array}$
Endgültige Antwort auf das Problem
$x^{3}+8x^{2}-3x+3$