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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)?

Accepted Answer

p(x) must be a factor of 3(x^4+6x^2+25)-(3x^4+4x^2+28x+5)=14x^2-28x+70=14(x^2-2x+5). Therefore p(x)=x^2 -2x+5 and p(1)=4. The answer is 4.