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