Question:
If $(x+a)$ is a factor of $\left(2 x^{2}+2 a x+5 x+10\right)$, find the value of $a .$
Solution:
Given: (x + a) is a factor of 2x2 + 2ax + 5x + 10
We have
$x+a=0$
$\Rightarrow x=-a$
Since, $(x+a)$ is a factor of $2 x^{2}+2 a x+5 x+10$
Hence, It will satisfy the above polynomial
$\therefore 2(-a)^{2}+2 a(-a)+5(-a)+10=0$
$\Rightarrow-5 a+10=0$
$\Rightarrow a=2$