Exercice
$\frac{x^4-5x^3+4x^2+7}{x+2}$
Solution étape par étape
1
Diviser $x^4-5x^3+4x^2+7$ par $x+2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}-7x^{2}+18x\phantom{;}-36\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}-5x^{3}+4x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}-7x^{3}+4x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}7x^{3}+14x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{3}+14x^{2}-;x^n;}\phantom{;}18x^{2}\phantom{-;x^n}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-18x^{2}-36x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-18x^{2}-36x\phantom{;}-;x^n-;x^n;}-36x\phantom{;}+7\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}36x\phantom{;}+72\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}36x\phantom{;}+72\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}79\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-7x^{2}+18x-36+\frac{79}{x+2}$
Réponse finale au problème
$x^{3}-7x^{2}+18x-36+\frac{79}{x+2}$