Hi,

An example:

To calculate $\displaystyle f(5)$ for $\displaystyle f(x)=x^3-3x^2+7x-4$ I can either subsitute $\displaystyle 5$ for $\displaystyle x$ and get 81, or I can divide the polynomial by $\displaystyle (x-5)$ and evaluate the remainder to get the same value.

This is really quite astounding. My reference(s) don't explain why this is true. I have given it some thought, but cannot figure out why this symetry (if it is a symetry) is true.

Any ideas?

Regards

Craig.