Let's say I'm given four points to use in Newton Interpolation, now suppose that the coefficient of my highest degree term $x^3$ is zero, does this tell me anything about the true error?
2026-03-28 04:42:50.1774672970
What does it mean if the last term of my Newton interpolating polynomial is zero?
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No, the $x^3$ term having a zero coefficient only means that these four points lie on one quadratic curve. Try generating 7 points from any random straight line and then interpolate, you'll get the same straight line back rather than a 6th degree polynomial.