Exercício
$\frac{m^5-32}{m+2}$
Solução explicada passo a passo
1
Dividimos polinômios, $m^5-32$ por $m+2$
$\begin{array}{l}\phantom{\phantom{;}m\phantom{;}+2;}{\phantom{;}m^{4}-2m^{3}+4m^{2}-8m\phantom{;}+16\phantom{;}\phantom{;}}\\\phantom{;}m\phantom{;}+2\overline{\smash{)}\phantom{;}m^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}}\\\phantom{\phantom{;}m\phantom{;}+2;}\underline{-m^{5}-2m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-m^{5}-2m^{4};}-2m^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n;}\underline{\phantom{;}2m^{4}+4m^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}2m^{4}+4m^{3}-;x^n;}\phantom{;}4m^{3}\phantom{-;x^n}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n;}\underline{-4m^{3}-8m^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-4m^{3}-8m^{2}-;x^n-;x^n;}-8m^{2}\phantom{-;x^n}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n-;x^n;}\underline{\phantom{;}8m^{2}+16m\phantom{;}\phantom{-;x^n}}\\\phantom{;;;\phantom{;}8m^{2}+16m\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}16m\phantom{;}-32\phantom{;}\phantom{;}\\\phantom{\phantom{;}m\phantom{;}+2-;x^n-;x^n-;x^n-;x^n;}\underline{-16m\phantom{;}-32\phantom{;}\phantom{;}}\\\phantom{;;;;-16m\phantom{;}-32\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}-64\phantom{;}\phantom{;}\\\end{array}$
2
Da divisão, obtemos o seguinte polinômio como resultado
$m^{4}-2m^{3}+4m^{2}-8m+16+\frac{-64}{m+2}$
Resposta final para o problema
$m^{4}-2m^{3}+4m^{2}-8m+16+\frac{-64}{m+2}$