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Turkey NMO 2008 1st Round - P03 (Algebra)

Source:

August 24, 2012
algebrapolynomial

Problem Statement

Let P(x)=1−x+x2−x3+⋯+x18−x19P(x) = 1-x+x^2-x^3+\dots+x^{18}-x^{19} and Q(x)=P(x−1)Q(x)=P(x-1). What is the coefficient of x2x^2 in polynomial QQ?
<spanclass=′latex−bold′>(A)</span> 840<spanclass=′latex−bold′>(B)</span> 816<spanclass=′latex−bold′>(C)</span> 969<spanclass=′latex−bold′>(D)</span> 1020<spanclass=′latex−bold′>(E)</span> 1140 <span class='latex-bold'>(A)</span>\ 840 \qquad<span class='latex-bold'>(B)</span>\ 816 \qquad<span class='latex-bold'>(C)</span>\ 969 \qquad<span class='latex-bold'>(D)</span>\ 1020 \qquad<span class='latex-bold'>(E)</span>\ 1140
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