Solve:-
$x^{3} - 3 x^{2} - 9 x - 5$

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Solution

$P (x) = x^{3} - 3 x^{2} - 9 x - 5$
$p (- 1) = - 1 - 3 + 9 - 5 = 0$
$∴ - 1$ is the root of $p (x)$
$x + 1$ divided $p (x)$
$x + 1) ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ x^{3} - 3 x^{3} - 9 x - 5 (x^{2} - 4 x - 5 x^{3} + x^{2} - -____________- 4 x^{2} - 9 x - {4 x}^{2} - 4 x + +_- 5 x - 5 - 5 x - 5___________x$
$x_{3} - 3 x^{2} - 9 x - 5 = (x + 1) (x^{2} - 4 x - 5)$
$= (x + 1) (x^{2} - 4 x + 2^{2} - 2^{2} - 5)$
$= (x + 1) (x^{2} + 4 - 4 x - 9)$
$= (x + 1) [(x - 2)^{2} - 3^{2}]$
$= (x + 1) (x - 2 + 3) (x - 2 - 3)$
$= (x + 1) (x + 1) (x - 5)$
$∴ x^{3} - 3 x^{2} - 9 x - 5 = (x + 1^{2}) (x - 5)$

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Solve: $x^{3} - 3 x^{2} - 9 x - 5$

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