Esercizio
$\left(\frac{x^5+x^4+7x^2-27x\:+\:10}{x^2-x\:+\:5}\right)$
Soluzione passo-passo
1
Dividere $x^5+x^4+7x^2-27x+10$ per $x^2-x+5$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}+5;}{\phantom{;}x^{3}+2x^{2}-3x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{5}+x^{4}\phantom{-;x^n}+7x^{2}-27x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5;}\underline{-x^{5}+x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}+x^{4}-5x^{3};}\phantom{;}2x^{4}-5x^{3}+7x^{2}-27x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5-;x^n;}\underline{-2x^{4}+2x^{3}-10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{4}+2x^{3}-10x^{2}-;x^n;}-3x^{3}-3x^{2}-27x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5-;x^n-;x^n;}\underline{\phantom{;}3x^{3}-3x^{2}+15x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}3x^{3}-3x^{2}+15x\phantom{;}-;x^n-;x^n;}-6x^{2}-12x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}6x^{2}-6x\phantom{;}+30\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}6x^{2}-6x\phantom{;}+30\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-18x\phantom{;}+40\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+2x^{2}-3x-6+\frac{-18x+40}{x^2-x+5}$
Risposta finale al problema
$x^{3}+2x^{2}-3x-6+\frac{-18x+40}{x^2-x+5}$