Übung
\frac{x^4 + 6x^3 - 8x^2 - 24x + 33}{x - 2}
Schritt-für-Schritt-Lösung
1
Mathematische Interpretation der Frage
$\frac{x^4+6x^3-8x^2-24x+33}{x-2}$
2
Teilen Sie $x^4+6x^3-8x^2-24x+33$ durch $x-2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{3}+8x^{2}+8x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}+6x^{3}-8x^{2}-24x\phantom{;}+33\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3};}\phantom{;}8x^{3}-8x^{2}-24x\phantom{;}+33\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-8x^{3}+16x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-8x^{3}+16x^{2}-;x^n;}\phantom{;}8x^{2}-24x\phantom{;}+33\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-8x^{2}+16x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-8x^{2}+16x\phantom{;}-;x^n-;x^n;}-8x\phantom{;}+33\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8x\phantom{;}-16\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}8x\phantom{;}-16\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}17\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+8x^{2}+8x-8+\frac{17}{x-2}$
Endgültige Antwort auf das Problem
$x^{3}+8x^{2}+8x-8+\frac{17}{x-2}$