Find the value of k, if $x + 3$ is a factor of $3 x^{2} + k x + 6$ .

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Solution

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

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