Exercice
$\frac{x^4-5x^2-8}{x+5}$
Solution étape par étape
1
Diviser $x^4-5x^2-8$ par $x+5$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{3}-5x^{2}+20x\phantom{;}-100\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-5x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-5x^{3};}-5x^{3}-5x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{3}+25x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+25x^{2}-;x^n;}\phantom{;}20x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-20x^{2}-100x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-20x^{2}-100x\phantom{;}-;x^n-;x^n;}-100x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}100x\phantom{;}+500\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}100x\phantom{;}+500\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}492\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-5x^{2}+20x-100+\frac{492}{x+5}$
Réponse finale au problème
$x^{3}-5x^{2}+20x-100+\frac{492}{x+5}$