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

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Solution

Let $p (x) = 3 x^{2} + m x + 6$
If $x + 3$ is a factor of p(x), then
$p (- 3) = 0$
$p (- 3) = 3 (- 3)^{2} + m (- 3) + 6 = 0$
$\Rightarrow 3 \times 9 - 3 m + 6 = 0$
$\Rightarrow 27 - 3 m + 6 = 0$
$\Rightarrow 3 m = 33$
$\Rightarrow m = 11$

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