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Cubic polynomial coefficients

Source: AMC 12B #16

February 20, 2014
algebrapolynomialsystem of equationsAMC

Problem Statement

Let PP be a cubic polynomial with P(0)=k,P(1)=2k,P(0) = k, P(1) = 2k, and P(−1)=3kP(-1) = 3k. What is P(2)+P(−2)P(2) + P(-2)?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>k<spanclass=′latex−bold′>(C)</span>6k<spanclass=′latex−bold′>(D)</span>7k<spanclass=′latex−bold′>(E)</span>14k <span class='latex-bold'>(A) </span>0 \qquad<span class='latex-bold'>(B) </span>k \qquad<span class='latex-bold'>(C) </span>6k \qquad<span class='latex-bold'>(D) </span>7k\qquad<span class='latex-bold'>(E) </span>14k\qquad
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