![\boxed{\sf \ a = 1 \ }](/tpl/images/0695/9413/d636e.png)
Step-by-step explanation:
let s assume that a >=0 so that we can take the square root
if
is a factor of this expression it means that
is a root of it
it comes
![2*(\sqrt{a})^4-2*a^2*(\sqrt{a})^2-3*\sqrt{a}+2*(\sqrt{a})^3-2(\sqrt{a})^2+3=0](/tpl/images/0695/9413/a11a6.png)
So
![2*a^2-2*a^3-3*\sqrt{a}+2*a*\sqrt{a}-2*a+3=0](/tpl/images/0695/9413/623ed.png)
we can notice that 1 is a trivial solution as
2-2-3+2-2+3=0
so the answer is 1
let s double check
if a =1
the expression is
![2x^4-2x^2-3x+2-2+3=2x^4-2x^2-3x+3](/tpl/images/0695/9413/8b93a.png)
and we can write
![2x^4-2x^2-3x+3=(x-1)(2x^3+2x^2-3)](/tpl/images/0695/9413/a6d2a.png)
so 1 is the correct answer