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P(x) divisible by x-2

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April 2, 2013
quadraticsVietaalgebrapolynomial

Problem Statement

Let P(x)=kx3+2k2x2+k3P(x)=kx^3+2k^2x^2+k^3. Find the sum of all real numbers kk for which x−2x-2 is a factor of P(x)P(x).
<spanclass=′latex−bold′>(A)</span>−8<spanclass=′latex−bold′>(B)</span>−4<spanclass=′latex−bold′>(C)</span>0<spanclass=′latex−bold′>(D)</span>5<spanclass=′latex−bold′>(E)</span>8<span class='latex-bold'>(A) </span>-8\qquad<span class='latex-bold'>(B) </span>-4\qquad<span class='latex-bold'>(C) </span>0\qquad<span class='latex-bold'>(D) </span>5\qquad<span class='latex-bold'>(E) </span>8
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