Esercizio
$\frac{4x^4+13x^3+28x^2+25x+12}{4x^2+5x+2}$
Soluzione passo-passo
1
Dividere $4x^4+13x^3+28x^2+25x+12$ per $4x^2+5x+2$
$\begin{array}{l}\phantom{\phantom{;}4x^{2}+5x\phantom{;}+2;}{\phantom{;}x^{2}+2x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}4x^{2}+5x\phantom{;}+2\overline{\smash{)}\phantom{;}4x^{4}+13x^{3}+28x^{2}+25x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x^{2}+5x\phantom{;}+2;}\underline{-4x^{4}-5x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{4}-5x^{3}-2x^{2};}\phantom{;}8x^{3}+26x^{2}+25x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+5x\phantom{;}+2-;x^n;}\underline{-8x^{3}-10x^{2}-4x\phantom{;}\phantom{-;x^n}}\\\phantom{;-8x^{3}-10x^{2}-4x\phantom{;}-;x^n;}\phantom{;}16x^{2}+21x\phantom{;}+12\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x^{2}+5x\phantom{;}+2-;x^n-;x^n;}\underline{-16x^{2}-20x\phantom{;}-8\phantom{;}\phantom{;}}\\\phantom{;;-16x^{2}-20x\phantom{;}-8\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}x\phantom{;}+4\phantom{;}\phantom{;}\\\end{array}$
$x^{2}+2x+4+\frac{x+4}{4x^2+5x+2}$
Risposta finale al problema
$x^{2}+2x+4+\frac{x+4}{4x^2+5x+2}$