Exercice
$\frac{2x^4-x^2+1}{x-7}$
Solution étape par étape
1
Diviser $2x^4-x^2+1$ par $x-7$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-7;}{\phantom{;}2x^{3}+14x^{2}+97x\phantom{;}+679\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-7\overline{\smash{)}\phantom{;}2x^{4}\phantom{-;x^n}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-7;}\underline{-2x^{4}+14x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+14x^{3};}\phantom{;}14x^{3}-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-7-;x^n;}\underline{-14x^{3}+98x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-14x^{3}+98x^{2}-;x^n;}\phantom{;}97x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-7-;x^n-;x^n;}\underline{-97x^{2}+679x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-97x^{2}+679x\phantom{;}-;x^n-;x^n;}\phantom{;}679x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-7-;x^n-;x^n-;x^n;}\underline{-679x\phantom{;}+4753\phantom{;}\phantom{;}}\\\phantom{;;;-679x\phantom{;}+4753\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}4754\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}+14x^{2}+97x+679+\frac{4754}{x-7}$
Réponse finale au problème
$2x^{3}+14x^{2}+97x+679+\frac{4754}{x-7}$