Question:
Divide $-x^{6}+2 x^{4}+4 x^{3}+2 x^{2}$ by $\sqrt{2} x^{2}$
Solution:
$\frac{-x^{6}+2 x^{4}+4 x^{3}+2 x^{2}}{\sqrt{2} x^{2}}$
$=\frac{-x^{6}}{\sqrt{2} x^{2}}+\frac{2 x^{4}}{\sqrt{2} x^{2}}+\frac{4 x^{3}}{\sqrt{2} x^{2}}+\frac{2 x^{2}}{\sqrt{2} x^{2}}$
$=\frac{-1}{\sqrt{2}} x^{(6-2)}+\sqrt{2} x^{(4-2)}+2 \sqrt{2} x^{(3-2)}+\sqrt{2} x^{(2-2)}$
$=\frac{-1}{\sqrt{2}} x^{4}+\sqrt{2} x^{2}+2 \sqrt{2} x+\sqrt{2}$
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