Exercice
$\frac{3x^4+2x^2-5x+3}{x+3}$
Solution étape par étape
1
Diviser $3x^4+2x^2-5x+3$ par $x+3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}3x^{3}-9x^{2}+29x\phantom{;}-92\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}+2x^{2}-5x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-3x^{4}-9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-9x^{3};}-9x^{3}+2x^{2}-5x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}9x^{3}+27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{3}+27x^{2}-;x^n;}\phantom{;}29x^{2}-5x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-29x^{2}-87x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-29x^{2}-87x\phantom{;}-;x^n-;x^n;}-92x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}92x\phantom{;}+276\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}92x\phantom{;}+276\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}279\phantom{;}\phantom{;}\\\end{array}$
$3x^{3}-9x^{2}+29x-92+\frac{279}{x+3}$
Réponse finale au problème
$3x^{3}-9x^{2}+29x-92+\frac{279}{x+3}$