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

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Solution

Let $P (x) = x^{3} - 3 x^{2} + 3 x + 7$

On applying integral root theorem

Constant term=7

Possible roots= $\frac{+}{} 1, \frac{+}{} 7$

P(-1)=-1–3–3+7=7–7=0

so x+1 is a factor of P(x)

$X^{3} + X^{2} - 4 X^{2} - 4 X + 7 X + 7$

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

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

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