Exercice
$\frac{x^4-2x^3-11x^2+30x-20}{x^2-x+3}$
Solution étape par étape
1
Diviser $x^4-2x^3-11x^2+30x-20$ par $x^2-x+3$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+3;}{\phantom{;}x^{2}-x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+3\overline{\smash{)}\phantom{;}x^{4}-2x^{3}-11x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+3;}\underline{-x^{4}+x^{3}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{3}-3x^{2};}-x^{3}-14x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+3-;x^n;}\underline{\phantom{;}x^{3}-x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}-x^{2}+3x\phantom{;}-;x^n;}-15x^{2}+33x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+3-;x^n-;x^n;}\underline{\phantom{;}15x^{2}-15x\phantom{;}+45\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}15x^{2}-15x\phantom{;}+45\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}18x\phantom{;}+25\phantom{;}\phantom{;}\\\end{array}$
$x^{2}-x-15+\frac{18x+25}{x^2-x+3}$
Réponse finale au problème
$x^{2}-x-15+\frac{18x+25}{x^2-x+3}$