Exercice
$\frac{\left(x^4-x^3+6x^2-60\right)}{\left(x+2\right)}$
Solution étape par étape
1
Diviser $x^4-x^3+6x^2-60$ par $x+2$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+2;}{\phantom{;}x^{3}-3x^{2}+12x\phantom{;}-24\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{4}-x^{3}+6x^{2}\phantom{-;x^n}-60\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+2;}\underline{-x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-2x^{3};}-3x^{3}+6x^{2}\phantom{-;x^n}-60\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n;}\underline{\phantom{;}3x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+6x^{2}-;x^n;}\phantom{;}12x^{2}\phantom{-;x^n}-60\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n;}\underline{-12x^{2}-24x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-12x^{2}-24x\phantom{;}-;x^n-;x^n;}-24x\phantom{;}-60\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}24x\phantom{;}+48\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}24x\phantom{;}+48\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-12\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-3x^{2}+12x-24+\frac{-12}{x+2}$
Réponse finale au problème
$x^{3}-3x^{2}+12x-24+\frac{-12}{x+2}$