Garvil's polynomial of degree 4

Algebra Level 5

A monic polynomial f(x) f(x ) of degree four satisfies f(1)=10f(1)=10, f(2)=20f(2)=20, and f(3)=30f(3)=30. Determine f(12)+f(8)19000.f(12)+f(-8)-19000.

This problem is posed by Garvil S.

Details and assumptions

A polynomial is monic if its leading coefficient is 1. For example, the polynomial x3+3x5 x^3 + 3x - 5 is monic but the polynomial x4+2x36 -x^4 + 2x^3 - 6 is not.

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