Exercice
$\frac{x^4-4x^3+2x-7}{x-2}$
Solution étape par étape
1
Diviser $x^4-4x^3+2x-7$ par $x-2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}x^{3}-2x^{2}-4x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}-4x^{3}\phantom{-;x^n}+2x\phantom{;}-7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3};}-2x^{3}\phantom{-;x^n}+2x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{\phantom{;}2x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}-4x^{2}-;x^n;}-4x^{2}+2x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}4x^{2}-8x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}4x^{2}-8x\phantom{;}-;x^n-;x^n;}-6x\phantom{;}-7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{\phantom{;}6x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}6x\phantom{;}-12\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-19\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-2x^{2}-4x-6+\frac{-19}{x-2}$
Réponse finale au problème
$x^{3}-2x^{2}-4x-6+\frac{-19}{x-2}$