The Universe of Discourse

Tue, 20 Feb 2007

A polynomial trivium
A couple of months ago I calculated the following polynomial—I forget why—and wrote it on my whiteboard. I want to erase the whiteboard, so I'm recording the polynomial here instead.

$${9\over 8}x^4 - {45\over 4}x^3 + 39{3\over8}x^2 - 54{1\over4}x + 27$$

The property this polynomial was designed to have is this: at x = 1, 2, 3, 4, it takes the values 2, 4, 6, 8. But at x=5 it gives not 10 but 37.

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