I'm supposed to use the Gram-Schmidt process to create Legrende polynomials. Usually when doing Gram-Schmidt, I first use it to create a set of orthogonal basises, then I divide every one of them by their norm to make the set orthonormal.

However, in this case, I suddently got to the point where I'm dividing a polynomial by zero, and that can't be right. I then tried to normalize each vector before proceeding to the next, and this time I didn't have the same problem, and I got the right answer in the end.

My question is basically, does this sometimes happen, that you can't create an orthogonal set of vectors first, or did I do something wrong with my calculations the first time?

Thanks!