Exercice
$\frac{x^4-x^3+5x+2}{x^2+x-1}$
Solution étape par étape
1
Diviser $x^4-x^3+5x+2$ par $x^2+x-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}-1;}{\phantom{;}x^{2}-2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{4}-x^{3}\phantom{-;x^n}+5x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-1;}\underline{-x^{4}-x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3}+x^{2};}-2x^{3}+x^{2}+5x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-1-;x^n;}\underline{\phantom{;}2x^{3}+2x^{2}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}+2x^{2}-2x\phantom{;}-;x^n;}\phantom{;}3x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}-1-;x^n-;x^n;}\underline{-3x^{2}-3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;;-3x^{2}-3x\phantom{;}+3\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$
$x^{2}-2x+3+\frac{5}{x^2+x-1}$
Réponse finale au problème
$x^{2}-2x+3+\frac{5}{x^2+x-1}$