Exercice
\frac{x^3 + 5x^2 - 5x - 21 }{x + 2}
Solution étape par étape
1
Interprétation mathématique de la question
$\frac{x^3+5x^2-5x-21}{x+2}$
2
Diviser $x^3+5x^2-5x-21$ par $x+2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{2}+3x\phantom{;}-11\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}+5x^{2}-5x\phantom{;}-21\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-2x^{2};}\phantom{;}3x^{2}-5x\phantom{;}-21\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{-3x^{2}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{2}-6x\phantom{;}-;x^n;}-11x\phantom{;}-21\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{\phantom{;}11x\phantom{;}+22\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}11x\phantom{;}+22\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$
$x^{2}+3x-11+\frac{1}{x+2}$
Réponse finale au problème
$x^{2}+3x-11+\frac{1}{x+2}$