Übung
$\frac{x^4-19x^2+7x+16}{x^2-3x-3}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $x^4-19x^2+7x+16$ durch $x^2-3x-3$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}-3;}{\phantom{;}x^{2}+3x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-19x^{2}+7x\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-3;}\underline{-x^{4}+3x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+3x^{3}+3x^{2};}\phantom{;}3x^{3}-16x^{2}+7x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-3-;x^n;}\underline{-3x^{3}+9x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{3}+9x^{2}+9x\phantom{;}-;x^n;}-7x^{2}+16x\phantom{;}+16\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}7x^{2}-21x\phantom{;}-21\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}7x^{2}-21x\phantom{;}-21\phantom{;}\phantom{;}-;x^n-;x^n;}-5x\phantom{;}-5\phantom{;}\phantom{;}\\\end{array}$
$x^{2}+3x-7+\frac{-5x-5}{x^2-3x-3}$
Endgültige Antwort auf das Problem
$x^{2}+3x-7+\frac{-5x-5}{x^2-3x-3}$