Esercizio
$\frac{2x^4+3x^3-x+1}{x-3}$
Soluzione passo-passo
1
Dividere $2x^4+3x^3-x+1$ per $x-3$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-3;}{\phantom{;}2x^{3}+9x^{2}+27x\phantom{;}+80\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-3\overline{\smash{)}\phantom{;}2x^{4}+3x^{3}\phantom{-;x^n}-x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}-3;}\underline{-2x^{4}+6x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+6x^{3};}\phantom{;}9x^{3}\phantom{-;x^n}-x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n;}\underline{-9x^{3}+27x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-9x^{3}+27x^{2}-;x^n;}\phantom{;}27x^{2}-x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n;}\underline{-27x^{2}+81x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-27x^{2}+81x\phantom{;}-;x^n-;x^n;}\phantom{;}80x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}-3-;x^n-;x^n-;x^n;}\underline{-80x\phantom{;}+240\phantom{;}\phantom{;}}\\\phantom{;;;-80x\phantom{;}+240\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}241\phantom{;}\phantom{;}\\\end{array}$
$2x^{3}+9x^{2}+27x+80+\frac{241}{x-3}$
Risposta finale al problema
$2x^{3}+9x^{2}+27x+80+\frac{241}{x-3}$