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