Solve : $x^{3} - 3 x^{2} - 9 x - 5 = 0$

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Solution

Clearly, $5$ satisfy the equation.So, $x - 5$ is the factor.

$x - 5$ $) x^{3} - 3 x^{2} - 9 x - 5 ($ $x^{2} + 2 x + 1$
$x^{3} - 5 x^{2}$
----------------------------
$2 x^{2} - 9 x$
$2 x^{2} - 10 x$
-----------------------------
$x - 5$
$x - 5$
-------------------------------
$0$

$x^{2} + 2 x + 1$

$x^{2} + x + x + 1$

$x (x + 1) + 1 (x + 1)$

$(x + 1) (x + 1)$

Therefore the factors are: $x = 5$ and $x = - 1$

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

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