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