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

Hint :
$$\begin{align}x^4 + 6x^2 + 25 &= x^4 + 10x^2 + 25 -4x^2 \\ &= (x^2+5)^2 - (2x)^2\\&=(x^2+2x+5)(x^2-2x+5) \\ &\end{align}$$
$$\begin{align}3x^4 + 4x^2 + 28x + 5 &= (x^2-2x+5)(3x^2+6x+1)\end{align} $$
