Find the value of $P(1)$

Question

Let $P (x) = x^2 + bx + c$, where $b$ and $c$ are integer.

If $P(x)$ is a factor of both $x^4 + 6x^2 + 25$ and $3x^4 + 4x^2 + 28x + 5$, find the value of $P(1)$.

I am not being able to solve this.Some hints/suggestions?

Tell me if I can edit to improve this question.I could'nt try much.Got stuck.

Answer 1

HINT :

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