Exercice
$\frac{x^4-8x^3+3x+10}{x+10}$
Solution étape par étape
1
Diviser $x^4-8x^3+3x+10$ par $x+10$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+10;}{\phantom{;}x^{3}-18x^{2}+180x\phantom{;}-1797\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+10\overline{\smash{)}\phantom{;}x^{4}-8x^{3}\phantom{-;x^n}+3x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+10;}\underline{-x^{4}-10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-10x^{3};}-18x^{3}\phantom{-;x^n}+3x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+10-;x^n;}\underline{\phantom{;}18x^{3}+180x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}18x^{3}+180x^{2}-;x^n;}\phantom{;}180x^{2}+3x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+10-;x^n-;x^n;}\underline{-180x^{2}-1800x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-180x^{2}-1800x\phantom{;}-;x^n-;x^n;}-1797x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+10-;x^n-;x^n-;x^n;}\underline{\phantom{;}1797x\phantom{;}+17970\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}1797x\phantom{;}+17970\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}17980\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-18x^{2}+180x-1797+\frac{17980}{x+10}$
Réponse finale au problème
$x^{3}-18x^{2}+180x-1797+\frac{17980}{x+10}$