Exercice
$\frac{\left(256-y^8\right)}{\left(2+y\right)}$
Solution étape par étape
1
Diviser $256-y^8$ par $2+y$
$\begin{array}{l}\phantom{\phantom{;}y\phantom{;}+2;}{-y^{7}+2y^{6}-4y^{5}+8y^{4}-16y^{3}+32y^{2}-64y\phantom{;}+128\phantom{;}\phantom{;}}\\\phantom{;}y\phantom{;}+2\overline{\smash{)}-y^{8}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+256\phantom{;}\phantom{;}}\\\phantom{\phantom{;}y\phantom{;}+2;}\underline{\phantom{;}y^{8}+2y^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}y^{8}+2y^{7};}\phantom{;}2y^{7}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n;}\underline{-2y^{7}-4y^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2y^{7}-4y^{6}-;x^n;}-4y^{6}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}4y^{6}+8y^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;\phantom{;}4y^{6}+8y^{5}-;x^n-;x^n;}\phantom{;}8y^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{-8y^{5}-16y^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-8y^{5}-16y^{4}-;x^n-;x^n-;x^n;}-16y^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}16y^{4}+32y^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;\phantom{;}16y^{4}+32y^{3}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}32y^{3}\phantom{-;x^n}\phantom{-;x^n}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-32y^{3}-64y^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;;;-32y^{3}-64y^{2}-;x^n-;x^n-;x^n-;x^n-;x^n;}-64y^{2}\phantom{-;x^n}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}64y^{2}+128y\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;;;\phantom{;}64y^{2}+128y\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}128y\phantom{;}+256\phantom{;}\phantom{;}\\\phantom{\phantom{;}y\phantom{;}+2-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-128y\phantom{;}-256\phantom{;}\phantom{;}}\\\phantom{;;;;;;;-128y\phantom{;}-256\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n-;x^n;}\\\end{array}$
$-y^{7}+2y^{6}-4y^{5}+8y^{4}-16y^{3}+32y^{2}-64y+128$
Réponse finale au problème
$-y^{7}+2y^{6}-4y^{5}+8y^{4}-16y^{3}+32y^{2}-64y+128$