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Source: AHSME 1986 problem 24

October 1, 2011
algebrapolynomialAMC

Problem Statement

Let p(x)=x2+bx+cp(x) = x^{2} + bx + c, where bb and cc are integers. If p(x)p(x) is a factor of both x^{4} + 6x^{2} + 25 \text{and}  3x^{4} + 4x^{2} + 28x + 5, what is p(1)p(1)?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 0\qquad<span class='latex-bold'>(B)</span>\ 1\qquad<span class='latex-bold'>(C)</span>\ 2\qquad<span class='latex-bold'>(D)</span>\ 4\qquad<span class='latex-bold'>(E)</span>\ 8