Find the value of $p$ , if the value of $x^{4} - 3 x^{3} - p x - 5$ is equal to $23$ when $x = - 2$ .

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Solution

Given expression $x^{4} - 3 x^{3} - p x - 5$ is equal to $23$

$x^{4} - 3 x^{3} - p x - 5 = 23$ [ $∵$ Given $x = - 2$ ]

$\Rightarrow (- 2)^{4} - 3 (- 2)^{3} - p (- 2) - 5 = 23$

$\Rightarrow 16 - 3 (- 8) + 2 p - 5 = 23$

$\Rightarrow 16 + 24 + 2 p - 5 = 23$

$\Rightarrow 40 - 5 + 2 p = 23$

$\Rightarrow 2 p = 23 - 35$

$\Rightarrow 2 p = - 12$

$\Rightarrow p = - 6$ .

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