Esercizio
$\frac{x^4-2x^3-15x^2+55x-270}{x-5}$
Soluzione passo-passo
1
Dividere $x^4-2x^3-15x^2+55x-270$ per $x-5$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-5;}{\phantom{;}x^{3}+3x^{2}\phantom{-;x^n}+55\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-5\overline{\smash{)}\phantom{;}x^{4}-2x^{3}-15x^{2}+55x\phantom{;}-270\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-5;}\underline{-x^{4}+5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+5x^{3};}\phantom{;}3x^{3}-15x^{2}+55x\phantom{;}-270\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n;}\underline{-3x^{3}+15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{3}+15x^{2}-;x^n;}\phantom{;}55x\phantom{;}-270\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-5-;x^n-;x^n;}\underline{-55x\phantom{;}+275\phantom{;}\phantom{;}}\\\phantom{;;-55x\phantom{;}+275\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}5\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+3x^{2}+55+\frac{5}{x-5}$
Risposta finale al problema
$x^{3}+3x^{2}+55+\frac{5}{x-5}$