Find factor $f(x)$ conmmon to two quartic equation Let $f(x) = x^2 + bx + c$, where $b, c ∈ R$. If f(x) is a factor of both $x^4 + 6x^2 + 25$ and $3x^4 + 4x^2 + 28x + 5$, then find $f(x)$
My approach ,on dividing both quartic equation by $f(x)$ remainder is zero, but not getting the answer

If is a factor of $x^4 + 6 x^2 + 25$ and $3 x^4 + 4 x^2 + 28 x + 5$
then it is a factor of
$$
3 (x^4 + 6 x^2 + 25) - (3 x^4 + 4 x^2 + 28 x + 5)=14 (5 - 2 x + x^2)
$$
