If $4 x^{4} + 7 x^{3} - 4 x^{2} - 7 x + p$ is completely divisible by $x^{3} - x$ , then find the value of p.

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Solution

The correct option is A 0
Let $q (x) = 4 x^{4} + 7 x^{3} - 4 x^{2} - 7 x + p$
Now, $x^{3} - x = x (x - 1) (x + 1)$
So, $x = 0$ is a factor of $q (x)$ .
$q (0) = 0 + 0 - 0 - 0 + p = 0$
$⟹ p = 0$

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