Esercizio
$\frac{\left(2x^4+3x^3-10x^2-3x+6\right)}{\left(x^2-2\right)}$
Soluzione passo-passo
1
Dividere $2x^4+3x^3-10x^2-3x+6$ per $x^2-2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2;}{\phantom{;}2x^{2}+3x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2\overline{\smash{)}\phantom{;}2x^{4}+3x^{3}-10x^{2}-3x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2;}\underline{-2x^{4}\phantom{-;x^n}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-2x^{4}+4x^{2};}\phantom{;}3x^{3}-6x^{2}-3x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2-;x^n;}\underline{-3x^{3}\phantom{-;x^n}+6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{3}+6x\phantom{;}-;x^n;}-6x^{2}+3x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2-;x^n-;x^n;}\underline{\phantom{;}6x^{2}\phantom{-;x^n}-12\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}6x^{2}-12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3x\phantom{;}-6\phantom{;}\phantom{;}\\\end{array}$
$2x^{2}+3x-6+\frac{3x-6}{x^2-2}$
Risposta finale al problema
$2x^{2}+3x-6+\frac{3x-6}{x^2-2}$