Esercizio
$\frac{x^4+x^3+x^2+x+2}{\left(x-1\right)}$
Soluzione passo-passo
1
Dividere $x^4+x^3+x^2+x+2$ per $x-1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x^{3}+2x^{2}+3x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{4}+x^{3}+x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{3};}\phantom{;}2x^{3}+x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-2x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}+2x^{2}-;x^n;}\phantom{;}3x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n;}\underline{-3x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}+3x\phantom{;}-;x^n-;x^n;}\phantom{;}4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{-4x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;;;-4x\phantom{;}+4\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}6\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+2x^{2}+3x+4+\frac{6}{x-1}$
Risposta finale al problema
$x^{3}+2x^{2}+3x+4+\frac{6}{x-1}$