Factorise: $x^{3} - 3 x^{2} + 3 x + 7$

(x - 1) (x^{2} - 4 x + 7)

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(x + 1) (x^{2} - 4 x + 7)

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(x + 1) (x^{2} + 4 x + 7)

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(x - 1) (x^{2} + 4 x + 7)

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Solution

The correct option is B $(x + 1) (x^{2} - 4 x + 7)$
$x^{3} - 3 x^{2} + 3 x + 7$
$= x^{3} - 3 x^{2} + 3 x - 1 + 8$
$= {(x - 1)}^{3} + {(2)}^{3}$
$= (x - 1 + 2) [{(x - 1)}^{2} - (x - 1) \times 2 + 4)]$
$= (x + 1) (x^{2} - 2 x + 1 - 2 x + 2 + 4)$
$= (x + 1) (x^{2} - 4 x + 7)$

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