Esercizio
$\frac{x^5+x^2+1}{x^2+x+1}$
Soluzione passo-passo
1
Dividere $x^5+x^2+1$ per $x^2+x+1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}{\phantom{;}x^{3}-x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{5}\phantom{-;x^n}\phantom{-;x^n}+x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1;}\underline{-x^{5}-x^{4}-x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-x^{4}-x^{3};}-x^{4}-x^{3}+x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{4}+x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{4}+x^{3}+x^{2}-;x^n;}\phantom{;}2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+1-;x^n-;x^n;}\underline{-2x^{2}-2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;-2x^{2}-2x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}-2x\phantom{;}-1\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-x^{2}+2+\frac{-2x-1}{x^2+x+1}$
Risposta finale al problema
$x^{3}-x^{2}+2+\frac{-2x-1}{x^2+x+1}$