Question

Factorize:
(a) x3-3x-1+3/x-1/x3​

Answer 1

SOLUTION

TO FACTORISE

$\displaystyle \sf{ {x}^{3} - 3x - 1 + \frac{3}{x} - \frac{1}{ {x}^{3} } \: }$

EVALUATION

$\displaystyle \sf{ {x}^{3} - 3x - 1 + \frac{3}{x} - \frac{1}{ {x}^{3} } \: }$

$= \displaystyle \sf{ {x}^{3} - 3x + \frac{3}{x} - \frac{1}{ {x}^{3} } - 1 \: }$

$= \displaystyle \sf{ {(x)}^{3} - 3. {x}^{2} . \frac{1}{x} + {3}.{x} . \frac{1}{ {x}^{2} } - { \bigg( \frac{1}{x} \bigg)}^{3} - 1 \: }$

$= \displaystyle \sf{ { \bigg(x - \frac{1}{x} \bigg)}^{3} - {(1)}^{3} \: }$

$= \displaystyle \sf{ \bigg(x - \frac{1}{x} - 1 \bigg) \Bigg[{ \bigg(x - \frac{1}{x} \bigg)}^{2} +\bigg(x - \frac{1}{x} \bigg) + {(1)}^{2} \Bigg] }$

$= \displaystyle \sf{ \bigg(x - \frac{1}{x} - 1 \bigg) \Bigg[{ \bigg(x - \frac{1}{x} \bigg)}^{2} +\bigg(x - \frac{1}{x} \bigg) + 1 \Bigg] }$

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