Esercizio
$\frac{x^{4}+4x^{3}+8x^{2}-7x+2}{x^{2}-2x-1}$
Soluzione passo-passo
1
Dividere $x^4+4x^3+8x^2-7x+2$ per $x^2-2x-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}-1;}{\phantom{;}x^{2}+6x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{4}+4x^{3}+8x^{2}-7x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-1;}\underline{-x^{4}+2x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+2x^{3}+x^{2};}\phantom{;}6x^{3}+9x^{2}-7x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-1-;x^n;}\underline{-6x^{3}+12x^{2}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-6x^{3}+12x^{2}+6x\phantom{;}-;x^n;}\phantom{;}21x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}-1-;x^n-;x^n;}\underline{-21x^{2}+42x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{;;-21x^{2}+42x\phantom{;}+21\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}41x\phantom{;}+23\phantom{;}\phantom{;}\\\end{array}$
$x^{2}+6x+21+\frac{41x+23}{x^2-2x-1}$
Risposta finale al problema
$x^{2}+6x+21+\frac{41x+23}{x^2-2x-1}$