Übung
$\frac{\left(81-x^{12}\right)}{3-x^3}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $81-x^{12}$ durch $3-x^3$
$\begin{array}{l}\phantom{-x^{3}+3;}{\phantom{;}x^{9}\phantom{-;x^n}\phantom{-;x^n}+3x^{6}\phantom{-;x^n}\phantom{-;x^n}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}+27\phantom{;}\phantom{;}}\\-x^{3}+3\overline{\smash{)}-x^{12}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+81\phantom{;}\phantom{;}}\\\phantom{-x^{3}+3;}\underline{\phantom{;}x^{12}\phantom{-;x^n}\phantom{-;x^n}-3x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{12}-3x^{9};}-3x^{9}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+81\phantom{;}\phantom{;}\\\phantom{-x^{3}+3-;x^n;}\underline{\phantom{;}3x^{9}\phantom{-;x^n}\phantom{-;x^n}-9x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{9}-9x^{6}-;x^n;}-9x^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+81\phantom{;}\phantom{;}\\\phantom{-x^{3}+3-;x^n-;x^n;}\underline{\phantom{;}9x^{6}\phantom{-;x^n}\phantom{-;x^n}-27x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}9x^{6}-27x^{3}-;x^n-;x^n;}-27x^{3}\phantom{-;x^n}\phantom{-;x^n}+81\phantom{;}\phantom{;}\\\phantom{-x^{3}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}27x^{3}\phantom{-;x^n}\phantom{-;x^n}-81\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}27x^{3}-81\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\\\end{array}$
$x^{9}+3x^{6}+9x^{3}+27$
Endgültige Antwort auf das Problem
$x^{9}+3x^{6}+9x^{3}+27$