Question

Let P(x) = x^2 + bx + c, where b and c are integers. If p(x) is a factor of both x^4 + 6x^2 +25 and 3x^4 + 4x^2 + 28x + 5, what is p(1)

Answer 1

i am fairly sure \(x^4 + 6x^2 +25 \) does not have any factors

Answer 2

\[x^4+6 x^2+25=\left(x^2-2 x+5\right) \left(x^2+2 x+5\right) \]\[3 x^4+4 x^2+28 x+5=\left(x^2-2 x+5\right) \left(3 x^2+6 x+1\right) \]\[p(x)=x^2-2 x+5 \]\[p(1) = 4\]