A Pre-RMO question! -6

Algebra Level 1

Cubic polynomial P(x)P(x) is such that P(0)=kP(0)=k, P(1)=2kP(1)=2k, P(1)=3kP(-1)=3k, and P(2)+P(2)=αk\\ P(2)+P(-2)=\alpha k, where α\alpha is a real number, find α\alpha.

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