Garvil's polynomial of degree 4

Algebra Level 5

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

This problem is posed by Garvil S.

Details and assumptions

A polynomial is monic if its leading coefficient is 1. For example, the polynomial \( x^3 + 3x - 5 \) is monic but the polynomial \( -x^4 + 2x^3 - 6 \) is not.

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