Exercício
$\frac{6x^5+7x^4-18x^3+10x^2+7x+2}{3x^3-x^2+2}$
Solução explicada passo a passo
1
Dividimos polinômios, $6x^5+7x^4-18x^3+10x^2+7x+2$ por $3x^3-x^2+2$
$\begin{array}{l}\phantom{\phantom{;}3x^{3}-x^{2}+2;}{\phantom{;}2x^{2}+3x\phantom{;}-5\phantom{;}\phantom{;}}\\\phantom{;}3x^{3}-x^{2}+2\overline{\smash{)}\phantom{;}6x^{5}+7x^{4}-18x^{3}+10x^{2}+7x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{3}-x^{2}+2;}\underline{-6x^{5}+2x^{4}\phantom{-;x^n}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{5}+2x^{4}-4x^{2};}\phantom{;}9x^{4}-18x^{3}+6x^{2}+7x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{3}-x^{2}+2-;x^n;}\underline{-9x^{4}+3x^{3}\phantom{-;x^n}-6x\phantom{;}\phantom{-;x^n}}\\\phantom{;-9x^{4}+3x^{3}-6x\phantom{;}-;x^n;}-15x^{3}+6x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{3}-x^{2}+2-;x^n-;x^n;}\underline{\phantom{;}15x^{3}-5x^{2}\phantom{-;x^n}+10\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}15x^{3}-5x^{2}+10\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}x^{2}+x\phantom{;}+12\phantom{;}\phantom{;}\\\end{array}$
2
Da divisão, obtemos o seguinte polinômio como resultado
$2x^{2}+3x-5+\frac{x^{2}+x+12}{3x^3-x^2+2}$
Resposta final para o problema
$2x^{2}+3x-5+\frac{x^{2}+x+12}{3x^3-x^2+2}$