Find the value of $P$ for which polynomial $x^{3} + x^{2} - 3 x - P$ is exactly divisible by polynomial $(x + 3)$ .

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Solution

Consider the given polynomial.

$\Rightarrow x^{3} + x^{2} - 3 x - P$

Therefore, consider the division shown below.

If $(x + 3)$ completely divides $x^{3} + x^{2} - 3 x - P$ , then

$- 9 - P = 0$

$P = - 9$

Hence, the required value of $P$ is $- 9$ .

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