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