Exercice
$\frac{x^4+x^3-2x^2+5x+3}{x^2+2}$
Solution étape par étape
1
Diviser $x^4+x^3-2x^2+5x+3$ par $x^2+2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}x^{2}+x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}x^{4}+x^{3}-2x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-x^{4}\phantom{-;x^n}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{2};}\phantom{;}x^{3}-4x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{-x^{3}\phantom{-;x^n}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{3}-2x\phantom{;}-;x^n;}-4x^{2}+3x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n-;x^n;}\underline{\phantom{;}4x^{2}\phantom{-;x^n}+8\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}4x^{2}+8\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3x\phantom{;}+11\phantom{;}\phantom{;}\\\end{array}$
$x^{2}+x-4+\frac{3x+11}{x^2+2}$
Réponse finale au problème
$x^{2}+x-4+\frac{3x+11}{x^2+2}$