Übung
\frac{x^3 + x^2 - 12x + 22}{x + 3}
Schritt-für-Schritt-Lösung
1
Mathematische Interpretation der Frage
$\frac{x^3+x^2-12x+22}{x+3}$
2
Teilen Sie $x^3+x^2-12x+22$ durch $x+3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{2}-2x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{3}+x^{2}-12x\phantom{;}+22\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-3x^{2};}-2x^{2}-12x\phantom{;}+22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}2x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}+6x\phantom{;}-;x^n;}-6x\phantom{;}+22\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}6x\phantom{;}+18\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}6x\phantom{;}+18\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}40\phantom{;}\phantom{;}\\\end{array}$
$x^{2}-2x-6+\frac{40}{x+3}$
Endgültige Antwort auf das Problem
$x^{2}-2x-6+\frac{40}{x+3}$