Divide -x^6+2x^4+4x^3+2x^2 by 2x^2. - Vidyadip

Question

Divide $-\text{x}^6+2\text{x}^4+4\text{x}^3+2\text{x}^2\text{ by }\sqrt{2}\text{x}^2.$

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Answer

$\frac{-\text{x}^6+2\text{x}^4+4\text{x}^3+2\text{x}^2}{\sqrt{2}\text{x}^2}$
$=\frac{-\text{x}^6}{\sqrt{2}\text{x}^2}+\frac{2\text{x}^4}{\sqrt{2}\text{x}^2}+\frac{4\text{x}^3}{\sqrt{2}\text{x}^2}+\frac{2\text{x}^2}{\sqrt{2}\text{x}^2}$
$=\frac{-1}{\sqrt{2}}\text{x}^{(6-2)}+\sqrt{2}\text{x}^{(4-2)}+2\sqrt{2}\text{x}^{(3-2)}+\sqrt{2}\text{x}^{(2-2)}$
$=\frac{-1}{\sqrt{2}}\text{x}^4+\sqrt{2}\text{x}^2+2\sqrt{2}\text{x}+\sqrt{2}$

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