Factorize $x^{4} - x^{3} - x^{2}$

x (x^{2} - x - 1)

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x (x - x^{2} - x^{3})

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x (x^{3} - x^{2})

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x^{2} (x^{2} - x - 1)

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Solution

The correct option is D $x^{2} (x^{2} - x - 1)$
Given, $x^{4} - x^{3} - x^{2}$
Here all the terms are unlike.
Only $x^{2}$ is common from all, so
$\Rightarrow x^{2} (x^{2} - x - 1)$

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If $x + \frac{1}{x} = 3$ , calculate $x^{2} + \frac{1}{x^{2}}, x^{3} + \frac{1}{x^{3}} a n d x^{4} + \frac{1}{x^{4}}$ .

\int (x + x^{2} + x^{3} + x^{4})

x \neq 0

x + \frac{1}{x} = 2

x^{2} + \frac{1}{x^{2}} = x^{3} + \frac{1}{x^{3}} = x^{4} + \frac{1}{x^{4}}

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