Exercice
$\frac{2x^4-x^3+x^2-10}{x+3}$
Solution étape par étape
1
Diviser $2x^4-x^3+x^2-10$ par $x+3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+3;}{\phantom{;}2x^{3}-7x^{2}+22x\phantom{;}-66\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+3\overline{\smash{)}\phantom{;}2x^{4}-x^{3}+x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+3;}\underline{-2x^{4}-6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-6x^{3};}-7x^{3}+x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n;}\underline{\phantom{;}7x^{3}+21x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}7x^{3}+21x^{2}-;x^n;}\phantom{;}22x^{2}\phantom{-;x^n}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n;}\underline{-22x^{2}-66x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-22x^{2}-66x\phantom{;}-;x^n-;x^n;}-66x\phantom{;}-10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+3-;x^n-;x^n-;x^n;}\underline{\phantom{;}66x\phantom{;}+198\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}66x\phantom{;}+198\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}188\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}-7x^{2}+22x-66+\frac{188}{x+3}$
Réponse finale au problème
$2x^{3}-7x^{2}+22x-66+\frac{188}{x+3}$