Polynomially Yours!

Algebra Level 4

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

Note-This question is taken from SOF-IMO

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