Exercice
$\frac{x^4-3x^2+2}{x+3}$
Solution étape par étape
1
Diviser $x^4-3x^2+2$ par $x+3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}x^{3}-3x^{2}+6x\phantom{;}-18\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-3x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-x^{4}-3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3};}-3x^{3}-3x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}3x^{3}+9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+9x^{2}-;x^n;}\phantom{;}6x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-6x^{2}-18x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-6x^{2}-18x\phantom{;}-;x^n-;x^n;}-18x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}18x\phantom{;}+54\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}18x\phantom{;}+54\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}56\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-3x^{2}+6x-18+\frac{56}{x+3}$
Réponse finale au problème
$x^{3}-3x^{2}+6x-18+\frac{56}{x+3}$