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: $$ x^4+6x^2+25 = (x^2+3)^2+16 $$ $$= (x^2+3+4i)(x^2+3-4i)$$
So, the roots of the first functions are$$ \pm 1\pm 2i$$
