Esercizio
$\frac{x^4-8x^3+3x+10}{x-10}$
Soluzione passo-passo
1
Dividere $x^4-8x^3+3x+10$ per $x-10$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-10;}{\phantom{;}x^{3}+2x^{2}+20x\phantom{;}+203\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-10\overline{\smash{)}\phantom{;}x^{4}-8x^{3}\phantom{-;x^n}+3x\phantom{;}+10\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-10;}\underline{-x^{4}+10x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}+10x^{3};}\phantom{;}2x^{3}\phantom{-;x^n}+3x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-10-;x^n;}\underline{-2x^{3}+20x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-2x^{3}+20x^{2}-;x^n;}\phantom{;}20x^{2}+3x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-10-;x^n-;x^n;}\underline{-20x^{2}+200x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-20x^{2}+200x\phantom{;}-;x^n-;x^n;}\phantom{;}203x\phantom{;}+10\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-10-;x^n-;x^n-;x^n;}\underline{-203x\phantom{;}+2030\phantom{;}\phantom{;}}\\\phantom{;;;-203x\phantom{;}+2030\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}2040\phantom{;}\phantom{;}\\\end{array}$
$x^{3}+2x^{2}+20x+203+\frac{2040}{x-10}$
Risposta finale al problema
$x^{3}+2x^{2}+20x+203+\frac{2040}{x-10}$