Exercice
$\frac{\left(4c^5-2c^3+3c\right)}{\left(c^2-c+2\right)}$
Solution étape par étape
1
Diviser $4c^5-2c^3+3c$ par $c^2-c+2$
$\begin{array}{l}\phantom{\phantom{;}c^{2}-c\phantom{;}+2;}{\phantom{;}4c^{3}+4c^{2}-6c\phantom{;}-14\phantom{;}\phantom{;}}\\\phantom{;}c^{2}-c\phantom{;}+2\overline{\smash{)}\phantom{;}4c^{5}\phantom{-;x^n}-2c^{3}\phantom{-;x^n}+3c\phantom{;}\phantom{-;x^n}}\\\phantom{\phantom{;}c^{2}-c\phantom{;}+2;}\underline{-4c^{5}+4c^{4}-8c^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4c^{5}+4c^{4}-8c^{3};}\phantom{;}4c^{4}-10c^{3}\phantom{-;x^n}+3c\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}c^{2}-c\phantom{;}+2-;x^n;}\underline{-4c^{4}+4c^{3}-8c^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4c^{4}+4c^{3}-8c^{2}-;x^n;}-6c^{3}-8c^{2}+3c\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}c^{2}-c\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}6c^{3}-6c^{2}+12c\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}6c^{3}-6c^{2}+12c\phantom{;}-;x^n-;x^n;}-14c^{2}+15c\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}c^{2}-c\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}14c^{2}-14c\phantom{;}+28\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}14c^{2}-14c\phantom{;}+28\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}c\phantom{;}+28\phantom{;}\phantom{;}\\\end{array}$
$4c^{3}+4c^{2}-6c-14+\frac{c+28}{c^2-c+2}$
Réponse finale au problème
$4c^{3}+4c^{2}-6c-14+\frac{c+28}{c^2-c+2}$