Show that $(x - 2)$ is a factor of $x^{3} - 3 x^{2} - 10 x + 24$

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Solution

$x^{3} - 3 x^{2} - 10 x + 24$
To show if $(x - 2)$ is a factor, it is enough to show that at $x = 2,$ value of the polynomial is zero.
$∴ {(2)}^{3} - 3 {(2)}^{2} - 10 (2) + 24$
$\Rightarrow 8 - 12 - 20 + 24 = 0$
Hence, $(x - 2)$ is a factor of polynomial.

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