# 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.

×