Exercice
$\frac{3x^4-2x^3+x+3}{x^2+2}$
Solution étape par étape
1
Diviser $3x^4-2x^3+x+3$ par $x^2+2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+2;}{\phantom{;}3x^{2}-2x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2\overline{\smash{)}\phantom{;}3x^{4}-2x^{3}\phantom{-;x^n}+x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2;}\underline{-3x^{4}\phantom{-;x^n}-6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-6x^{2};}-2x^{3}-6x^{2}+x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n;}\underline{\phantom{;}2x^{3}\phantom{-;x^n}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}+4x\phantom{;}-;x^n;}-6x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2-;x^n-;x^n;}\underline{\phantom{;}6x^{2}\phantom{-;x^n}+12\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}6x^{2}+12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5x\phantom{;}+15\phantom{;}\phantom{;}\\\end{array}$
$3x^{2}-2x-6+\frac{5x+15}{x^2+2}$
Réponse finale au problème
$3x^{2}-2x-6+\frac{5x+15}{x^2+2}$