Esercizio
$\frac{x^5+2x^4-7x^2-19x+15}{\:x^2+2x+5}$
Soluzione passo-passo
1
Dividere $x^5+2x^4-7x^2-19x+15$ per $x^2+2x+5$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+2x\phantom{;}+5;}{\phantom{;}x^{3}\phantom{-;x^n}-5x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+2x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{5}+2x^{4}\phantom{-;x^n}-7x^{2}-19x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}+5;}\underline{-x^{5}-2x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{5}-2x^{4}-5x^{3};}-5x^{3}-7x^{2}-19x\phantom{;}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}+5-;x^n;}\underline{\phantom{;}5x^{3}+10x^{2}+25x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+10x^{2}+25x\phantom{;}-;x^n;}\phantom{;}3x^{2}+6x\phantom{;}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+2x\phantom{;}+5-;x^n-;x^n;}\underline{-3x^{2}-6x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;;-3x^{2}-6x\phantom{;}-15\phantom{;}\phantom{;}-;x^n-;x^n;}\\\end{array}$
Risposta finale al problema
$x^{3}-5x+3$