I found a profound paper written by Professor Lloyd N. Trefethen entitled Six Myths of Polynomial Interpolation and Quadrature. This paper is profound because it goes against a lot of the mainstream things that I have learned related to polynomials. After watching Professor Trefethen’s lectures, I found that he is right and knows what he is talking about. Read the paper. It is worth your time.

The paper is here if it is ever removed from the link above.
mythspaper