Polynomially Yours!

Algebra Level 4

If f(x)=x2+bx+cf(x)=x^{2}+bx+c where b,cb,c are integers and it is given that f(x)f(x) perfectly divides x4+6x2+25x^{4}+6x^{2}+25 and 3x4+4x2+28x+53x^{4}+4x^{2}+28x+5, what is the value of f(1)?f(1)?

Note-This question is taken from SOF-IMO

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