Esercizio
$\frac{x^4-7x^2+5x\:-6}{x^2-x\:-1}$
Soluzione passo-passo
1
Dividere $x^4-7x^2+5x-6$ per $x^2-x-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-x\phantom{;}-1;}{\phantom{;}x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}-7x^{2}+5x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-x\phantom{;}-1;}\underline{-x^{4}+x^{3}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+x^{3}+x^{2};}\phantom{;}x^{3}-6x^{2}+5x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}-1-;x^n;}\underline{-x^{3}+x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{3}+x^{2}+x\phantom{;}-;x^n;}-5x^{2}+6x\phantom{;}-6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}5x^{2}-5x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}5x^{2}-5x\phantom{;}-5\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}x\phantom{;}-11\phantom{;}\phantom{;}\\\end{array}$
$x^{2}+x-5+\frac{x-11}{x^2-x-1}$
Risposta finale al problema
$x^{2}+x-5+\frac{x-11}{x^2-x-1}$