Exercice
$\frac{x^4+3x^3+3x^2+3x+2}{x-2}$
Solution étape par étape
1
Diviser $x^4+3x^3+3x^2+3x+2$ par $x-2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{3}+5x^{2}+13x\phantom{;}+29\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}+3x^{3}+3x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3};}\phantom{;}5x^{3}+3x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-5x^{3}+10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-5x^{3}+10x^{2}-;x^n;}\phantom{;}13x^{2}+3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-13x^{2}+26x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-13x^{2}+26x\phantom{;}-;x^n-;x^n;}\phantom{;}29x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-29x\phantom{;}+58\phantom{;}\phantom{;}}\\\phantom{;;;-29x\phantom{;}+58\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}60\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+5x^{2}+13x+29+\frac{60}{x-2}$
Réponse finale au problème
$x^{3}+5x^{2}+13x+29+\frac{60}{x-2}$