Exercício
$\frac{6x^5+4x^4+9x^3-1}{2x^3-1}$
Solução explicada passo a passo
1
Dividimos polinômios, $6x^5+4x^4+9x^3-1$ por $2x^3-1$
$\begin{array}{l}\phantom{\phantom{;}2x^{3}-1;}{\phantom{;}3x^{2}+2x\phantom{;}+\frac{9}{2}\phantom{;}\phantom{;}}\\\phantom{;}2x^{3}-1\overline{\smash{)}\phantom{;}6x^{5}+4x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{3}-1;}\underline{-6x^{5}\phantom{-;x^n}\phantom{-;x^n}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{5}+3x^{2};}\phantom{;}4x^{4}+9x^{3}+3x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{3}-1-;x^n;}\underline{-4x^{4}\phantom{-;x^n}\phantom{-;x^n}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{4}+2x\phantom{;}-;x^n;}\phantom{;}9x^{3}+3x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{3}-1-;x^n-;x^n;}\underline{-9x^{3}\phantom{-;x^n}\phantom{-;x^n}+\frac{9}{2}\phantom{;}\phantom{;}}\\\phantom{;;-9x^{3}+\frac{9}{2}\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3x^{2}+2x\phantom{;}+\frac{7}{2}\phantom{;}\phantom{;}\\\end{array}$
2
Da divisão, obtemos o seguinte polinômio como resultado
$3x^{2}+2x+\frac{9}{2}+\frac{3x^{2}+2x+\frac{7}{2}}{2x^3-1}$
Resposta final para o problema
$3x^{2}+2x+\frac{9}{2}+\frac{3x^{2}+2x+\frac{7}{2}}{2x^3-1}$