Final Answer
$4x^{2}-2x+1+\frac{-1}{2x+1}$
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Step-by-step Solution
Specify the solving method
1
Divide $8x^3$ by $2x+1$
$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+1;}{\phantom{;}4x^{2}-2x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+1\overline{\smash{)}\phantom{;}8x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}2x\phantom{;}+1;}\underline{-8x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-8x^{3}-4x^{2};}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n;}\underline{\phantom{;}4x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{2}+2x\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}2x\phantom{;}+1-;x^n-;x^n;}\underline{-2x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;-2x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n;}-1\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$4x^{2}-2x+1+\frac{-1}{2x+1}$
Final Answer
$4x^{2}-2x+1+\frac{-1}{2x+1}$