Exercice
$\frac{x^4-x^3+7x^2-15}{x^2+2}$
Solution étape par étape
1
Diviser $x^4-x^3+7x^2-15$ par $x^2+2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}x^{2}-x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}x^{4}-x^{3}+7x^{2}\phantom{-;x^n}-15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-x^{4}\phantom{-;x^n}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{2};}-x^{3}+5x^{2}\phantom{-;x^n}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{\phantom{;}x^{3}\phantom{-;x^n}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+2x\phantom{;}-;x^n;}\phantom{;}5x^{2}+2x\phantom{;}-15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n-;x^n;}\underline{-5x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}}\\\phantom{;;-5x^{2}-10\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2x\phantom{;}-25\phantom{;}\phantom{;}\\\end{array}$
$x^{2}-x+5+\frac{2x-25}{x^2+2}$
Réponse finale au problème
$x^{2}-x+5+\frac{2x-25}{x^2+2}$