If $(x + 2)$ is a factor of $(x^{4} - x^{2} - a)$ , then find $a$ .

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Solution

Given: $(x + 2)$ is a factor of $(x^{4} - x^{2} - a)$

$\Rightarrow x = - 2$ is a zero of $x^{4} - x^{2} - a$

$\Rightarrow (- 2)^{4} - (- 2)^{2} - a = 0$

$\Rightarrow 16 - 4 - a = 0$

$\Rightarrow a = 12$

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