If $x + a$ is one of the factors of $p (x) = 2 x^{2} + 2 a x + 5 x + 10$ , then find $a$ .

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Solution

$P (x) = 2 x^{2} + 2 a x + 5 x + 10$
Given $x + a$ is the factor of $p (x)$
$\Rightarrow p (- a) = 0$
$\Rightarrow 2 (- a)^{2} + 2 a (- a) + 5 (- a) + 10 = 0$
$\Rightarrow 2 a^{2} - 2 a^{2} - 5 a + 10 = 0$
$\Rightarrow - 5 a + 10 = 0$
$\Rightarrow - 5 a = - 10$
$\Rightarrow a = 2$

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