Esercizio
$\frac{x^4+3x^3-2x^2+1}{x+5}$
Soluzione passo-passo
1
Dividere $x^4+3x^3-2x^2+1$ per $x+5$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+5;}{\phantom{;}x^{3}-2x^{2}+8x\phantom{;}-40\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+5\overline{\smash{)}\phantom{;}x^{4}+3x^{3}-2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+5;}\underline{-x^{4}-5x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-5x^{3};}-2x^{3}-2x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n;}\underline{\phantom{;}2x^{3}+10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{3}+10x^{2}-;x^n;}\phantom{;}8x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n;}\underline{-8x^{2}-40x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-8x^{2}-40x\phantom{;}-;x^n-;x^n;}-40x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+5-;x^n-;x^n-;x^n;}\underline{\phantom{;}40x\phantom{;}+200\phantom{;}\phantom{;}}\\\phantom{;;;\phantom{;}40x\phantom{;}+200\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}201\phantom{;}\phantom{;}\\\end{array}$
$x^{3}-2x^{2}+8x-40+\frac{201}{x+5}$
Risposta finale al problema
$x^{3}-2x^{2}+8x-40+\frac{201}{x+5}$