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