Exercice
$\frac{x^4-2x^3+2x-1}{x-3}$
Solution étape par étape
1
Diviser $x^4-2x^3+2x-1$ par $x-3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}x^{3}+x^{2}+3x\phantom{;}+11\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}x^{4}-2x^{3}\phantom{-;x^n}+2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-x^{4}+3x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+3x^{3};}\phantom{;}x^{3}\phantom{-;x^n}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-x^{3}+3x^{2}-;x^n;}\phantom{;}3x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-3x^{2}+9x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}+9x\phantom{;}-;x^n-;x^n;}\phantom{;}11x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-11x\phantom{;}+33\phantom{;}\phantom{;}}\\\phantom{;;;-11x\phantom{;}+33\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}32\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+x^{2}+3x+11+\frac{32}{x-3}$
Réponse finale au problème
$x^{3}+x^{2}+3x+11+\frac{32}{x-3}$