olymmath

AIME 2007a Problem 8

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The polynomial P(x)P(x) is cubic. What is the largest value of kk for which the polynomials Q1(x)=x2+(k−29)x−kQ_1(x) = x^2 + (k-29)x - k and Q2(x)=2x2+(2k−43)x+kQ_2(x) = 2x^2+ (2k-43)x + k are both factors of P(x)P(x)?

Dataset text AIME 1983 to 2026. Quoted with source.

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