Exercice
$\frac{\left(2x^6+2x^5-5x^4-3x^3+x^2+4x-3\right)}{-2+x}$
Solution étape par étape
1
Diviser $2x^6+2x^5-5x^4-3x^3+x^2+4x-3$ par $-2+x$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-2;}{\phantom{;}2x^{5}+6x^{4}+7x^{3}+11x^{2}+23x\phantom{;}+50\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-2\overline{\smash{)}\phantom{;}2x^{6}+2x^{5}-5x^{4}-3x^{3}+x^{2}+4x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-2;}\underline{-2x^{6}+4x^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{6}+4x^{5};}\phantom{;}6x^{5}-5x^{4}-3x^{3}+x^{2}+4x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n;}\underline{-6x^{5}+12x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-6x^{5}+12x^{4}-;x^n;}\phantom{;}7x^{4}-3x^{3}+x^{2}+4x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n;}\underline{-7x^{4}+14x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-7x^{4}+14x^{3}-;x^n-;x^n;}\phantom{;}11x^{3}+x^{2}+4x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-11x^{3}+22x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;;-11x^{3}+22x^{2}-;x^n-;x^n-;x^n;}\phantom{;}23x^{2}+4x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n;}\underline{-23x^{2}+46x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;;-23x^{2}+46x\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}50x\phantom{;}-3\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-2-;x^n-;x^n-;x^n-;x^n-;x^n;}\underline{-50x\phantom{;}+100\phantom{;}\phantom{;}}\\\phantom{;;;;;-50x\phantom{;}+100\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n-;x^n;}\phantom{;}97\phantom{;}\phantom{;}\\\end{array}$
$2x^{5}+6x^{4}+7x^{3}+11x^{2}+23x+50+\frac{97}{-2+x}$
Réponse finale au problème
$2x^{5}+6x^{4}+7x^{3}+11x^{2}+23x+50+\frac{97}{-2+x}$