If $x - 3$ is a factor of $x^{3} + 3 x^{2} + 3 x + p$ , then find the value of $p$ .

- 45

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11

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- 63

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67

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Solution

The correct option is D $- 63$
Let us say, $f (x) = x^{3} + 3 x^{2} + 3 x + p$ .

By using factor theorem, if $x - 3$ is a factor of $f (x)$ , then $f (3) = 0.$
So,
$\Rightarrow 3^{3} + 3 \times 3^{2} + 3 \times 3 + p = 0$
$\Rightarrow 27 + 27 + 9 + p = 0$
$\Rightarrow p = - 63$

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