Check the validity of the statement:
$(x + 2)$ is a factor of $p (x) = x^{3} + x^{2} + x + 2$ .

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Solution

To check:
$(x + 2)$ is a factor of $p (x) = x^{3} + x^{2} + x + 2$

Putting,
$x + 2 = 0$
$\Rightarrow x = - 2$

Putting value of $x = - 2$ in $p (x)$

$p (- 2) = {(- 2)}^{3} + {(- 2)}^{2} + (- 2) + 2$
$= - 8 + 4 - 2 + 2$
$= - 4$
It is not equal to $0$

Hence, $x + 2$ is not a factor of $p (x)$ .

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