If (x+a) is a factor of $(2 x^{2} + 2 a x + 5 x + 10)$ , find the value of a.

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Solution

$x + a$ is a factor of $2 x^{2} + 2 a x + 5 x + 10$
$∴ x + a = 0$
$x = - a$
$f (- a) = 0;$
Substituting values,
$2 (- a) ² + 2 (a) (- a) + 5 (- a) + 10 = 0$
$2 a ² - 2 a ² - 5 a + 10 = 0$
$- 5 a + 10 = 0$
$∴ a = 2$

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