I dont think this would fall under the catagory of discrete mathematics.
I am not sure exactly what you want, but the first thing that came to my mind was this...
let . This set spans because any polynomial fucntion in can be written as,
So, in your example, your basis is the set in . So any polynimial of degree 5 can be created by these vectors. Since you have coeficients we can write which is your polynomial. Thus any polynomial or the form can be created from the set S. The only thing that changes are your coeficients , so I guess you could just list them in a set.
Thats my stab at it.