Esercizio
$\frac{\left(3x^4+x^3+5x^2+x-5\right)}{\left(x^2-3x-1\right)}$
Soluzione passo-passo
1
Dividere $3x^4+x^3+5x^2+x-5$ per $x^2-3x-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-3x\phantom{;}-1;}{\phantom{;}3x^{2}+10x\phantom{;}+38\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3x\phantom{;}-1\overline{\smash{)}\phantom{;}3x^{4}+x^{3}+5x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-1;}\underline{-3x^{4}+9x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+9x^{3}+3x^{2};}\phantom{;}10x^{3}+8x^{2}+x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-1-;x^n;}\underline{-10x^{3}+30x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;-10x^{3}+30x^{2}+10x\phantom{;}-;x^n;}\phantom{;}38x^{2}+11x\phantom{;}-5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3x\phantom{;}-1-;x^n-;x^n;}\underline{-38x^{2}+114x\phantom{;}+38\phantom{;}\phantom{;}}\\\phantom{;;-38x^{2}+114x\phantom{;}+38\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}125x\phantom{;}+33\phantom{;}\phantom{;}\\\end{array}$
$3x^{2}+10x+38+\frac{125x+33}{x^2-3x-1}$
Risposta finale al problema
$3x^{2}+10x+38+\frac{125x+33}{x^2-3x-1}$