Question

x3 - x2 - x+1
$x3 - x2 - x + 1$
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Answer 1

We have,

$\quad \: {x}^{3} - {x}^{2} - x + 1 \\ \\ = x( {x}^{2} ) - 1( {x}^{2} ) - 1(x) - 1( - 1) \\ \\ = {x}^{2} (x - 1) - 1(x - 1) \\ \\ = (x - 1)( {x}^{2} - 1) \\ \\ = (x - 1) \left[ {(x)}^{2} - {(1)}^{2} \right] \\ \\ = (x - 1) \left[ (x - 1)(x + 1) \right] \\ \\ = (x - 1)(x - 1)(x + 1) \\ \\ = {(x - 1)}^{2} (x + 1)$

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