Explain this proof of polynomial congruences by George Andrews.
I don't get when it says. "Furthermore, g(x) is a polynomial of degree less than k, because the leading term aₒ x^k of f(x) is cancelled by the term aₒ x^k in the product to the right."

Wouldn't that be true only if x is NONE of the w1, w2, ..., wk???

Question

Explain this proof of polynomial congruences by George Andrews. 
I don't get when it says. "Furthermore, g(x) is a polynomial of degree less than k, because the leading term aₒ x^k of f(x) is cancelled by the term aₒ x^k in the product to the right."

Wouldn't that be true only if x is NONE of the w1, w2, ..., wk???

anonymous · Answer

https://books.google.com/books?id=eVwvvwZeBf4C&lpg=PA58&pg=PA72#v=onepage&q&f=false