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