Exercice
$\frac{\left(a^4-2a^3-11a^2+30a-20\right)}{\left(a^2+3a-2\right)}$
Solution étape par étape
1
Diviser $a^4-2a^3-11a^2+30a-20$ par $a^2+3a-2$
$\begin{array}{l}\phantom{\phantom{;}a^{2}+3a\phantom{;}-2;}{\phantom{;}a^{2}-5a\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}a^{2}+3a\phantom{;}-2\overline{\smash{)}\phantom{;}a^{4}-2a^{3}-11a^{2}+30a\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a^{2}+3a\phantom{;}-2;}\underline{-a^{4}-3a^{3}+2a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-a^{4}-3a^{3}+2a^{2};}-5a^{3}-9a^{2}+30a\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}a^{2}+3a\phantom{;}-2-;x^n;}\underline{\phantom{;}5a^{3}+15a^{2}-10a\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5a^{3}+15a^{2}-10a\phantom{;}-;x^n;}\phantom{;}6a^{2}+20a\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}a^{2}+3a\phantom{;}-2-;x^n-;x^n;}\underline{-6a^{2}-18a\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;-6a^{2}-18a\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2a\phantom{;}-8\phantom{;}\phantom{;}\\\end{array}$
$a^{2}-5a+6+\frac{2a-8}{a^2+3a-2}$
Réponse finale au problème
$a^{2}-5a+6+\frac{2a-8}{a^2+3a-2}$