Exercice
$\frac{\left(a^4-6a^3+2a^2+3a-4\right)}{\left(a^2-a+2\right)}$
Solution étape par étape
1
Diviser $a^4-6a^3+2a^2+3a-4$ par $a^2-a+2$
$\begin{array}{l}\phantom{\phantom{;}a^{2}-a\phantom{;}+2;}{\phantom{;}a^{2}-5a\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}a^{2}-a\phantom{;}+2\overline{\smash{)}\phantom{;}a^{4}-6a^{3}+2a^{2}+3a\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a^{2}-a\phantom{;}+2;}\underline{-a^{4}+a^{3}-2a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-a^{4}+a^{3}-2a^{2};}-5a^{3}\phantom{-;x^n}+3a\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}a^{2}-a\phantom{;}+2-;x^n;}\underline{\phantom{;}5a^{3}-5a^{2}+10a\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5a^{3}-5a^{2}+10a\phantom{;}-;x^n;}-5a^{2}+13a\phantom{;}-4\phantom{;}\phantom{;}\\\phantom{\phantom{;}a^{2}-a\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}5a^{2}-5a\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}5a^{2}-5a\phantom{;}+10\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}8a\phantom{;}+6\phantom{;}\phantom{;}\\\end{array}$
$a^{2}-5a-5+\frac{8a+6}{a^2-a+2}$
Réponse finale au problème
$a^{2}-5a-5+\frac{8a+6}{a^2-a+2}$