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Question
Divide\[- x^6 + 2 x^4 + 4 x^3 + 2 x^2\ \text{by} \sqrt{2} x^2\]
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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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