Exercice
$\frac{\left(2x^4+5x^3+4x^2-x-1\:\right)}{\left(2x+1\right)}$
Solution étape par étape
1
Diviser $2x^4+5x^3+4x^2-x-1$ par $2x+1$
$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+1;}{\phantom{;}x^{3}+2x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+1\overline{\smash{)}\phantom{;}2x^{4}+5x^{3}+4x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+1;}\underline{-2x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}-x^{3};}\phantom{;}4x^{3}+4x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n;}\underline{-4x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-4x^{3}-2x^{2}-;x^n;}\phantom{;}2x^{2}-x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n;}\underline{-2x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-2x^{2}-x\phantom{;}-;x^n-;x^n;}-2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{\phantom{;}2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}2x\phantom{;}+1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\\\end{array}$
Réponse finale au problème
$x^{3}+2x^{2}+x-1$