If $x + 3$ is a factor of $3 x^{2} + k x + 6$ , then the value of $k$ is

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Solution

Let $p (x) = 3 x^{2} + k x + 6$
Given, $x + 3$ is a factor of $p (x)$ .
$\Rightarrow p (- 3) = 0$
$\Rightarrow p (- 3) = 3 (- 3)^{2} + k (- 3) + 6 = 0$
$\Rightarrow 3 k = 33$
$\Rightarrow k = 11$

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