Übung
$\frac{\left(2x^4-5x^3+7x^2-3x+8\right)}{x-4}$
Schritt-für-Schritt-Lösung
1
Teilen Sie $2x^4-5x^3+7x^2-3x+8$ durch $x-4$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-4;}{\phantom{;}2x^{3}+3x^{2}+19x\phantom{;}+73\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-4\overline{\smash{)}\phantom{;}2x^{4}-5x^{3}+7x^{2}-3x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-4;}\underline{-2x^{4}+8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+8x^{3};}\phantom{;}3x^{3}+7x^{2}-3x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n;}\underline{-3x^{3}+12x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}+12x^{2}-;x^n;}\phantom{;}19x^{2}-3x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n;}\underline{-19x^{2}+76x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-19x^{2}+76x\phantom{;}-;x^n-;x^n;}\phantom{;}73x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-4-;x^n-;x^n-;x^n;}\underline{-73x\phantom{;}+292\phantom{;}\phantom{;}}\\\phantom{;;;-73x\phantom{;}+292\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}300\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}+3x^{2}+19x+73+\frac{300}{x-4}$
Endgültige Antwort auf das Problem
$2x^{3}+3x^{2}+19x+73+\frac{300}{x-4}$