Determine which of the following polynomial has

Let $p(x)=x^{5}-4 a^{2} x^{3}+2 x+2 a+3$

Since, $x+2 a$ is a factor of $p(x)$, then put $p(-2 a)=0$

$\therefore \quad(-2 a)^{5}-4 a^{2}(-2 a)^{3}+2(-2 a)+2 a+3=0$

$\Rightarrow \quad-32 a^{5}+32 a^{5}-4 a+2 a+3=0$

$\Rightarrow \quad-2 a+3=0$

$\Rightarrow \quad 2 a=3$

$\therefore$       $a=\frac{3}{2}$

Hence, the value of $a$ is $\frac{3}{2}$.