Esercizio
$\frac{243a^5-1}{3a-1}$
Soluzione passo-passo
1
Dividere $243a^5-1$ per $3a-1$
$\begin{array}{l}\phantom{\phantom{;}3a\phantom{;}-1;}{\phantom{;}81a^{4}+27a^{3}+9a^{2}+3a\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}3a\phantom{;}-1\overline{\smash{)}\phantom{;}243a^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3a\phantom{;}-1;}\underline{-243a^{5}+81a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-243a^{5}+81a^{4};}\phantom{;}81a^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}3a\phantom{;}-1-;x^n;}\underline{-81a^{4}+27a^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-81a^{4}+27a^{3}-;x^n;}\phantom{;}27a^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}3a\phantom{;}-1-;x^n-;x^n;}\underline{-27a^{3}+9a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-27a^{3}+9a^{2}-;x^n-;x^n;}\phantom{;}9a^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}3a\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{-9a^{2}+3a\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-9a^{2}+3a\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}3a\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}3a\phantom{;}-1-;x^n-;x^n-;x^n-;x^n;}\underline{-3a\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;;;;-3a\phantom{;}+1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\\\end{array}$
$81a^{4}+27a^{3}+9a^{2}+3a+1$
Risposta finale al problema
$81a^{4}+27a^{3}+9a^{2}+3a+1$