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

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Solution

Given: $(x + a)$ is a factor of $2 x^{2} + 2 a x + 5 x + 10$
So, we have
$x + a = 0 \Rightarrow x = - a$
Now, It will satisfy the above polynomial.
Therefore, we will get
$2 {(- a)}^{2} + 2 a (- a) + 5 (- a) + 10 = 0 \Rightarrow 2 a^{2} - 2 a^{2} - 5 a + 10 = 0 \Rightarrow - 5 a = - 10 \Rightarrow a = 2$

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