Sec4.3, 09/29/09

- i did not understand the corollary 4.19, where it says Let F be an infinite field and f(x), g(x) are in F[x] then f(x) and g(x) induces same function from F to F if and only if f(x)=g(x) in F[x]. what does it actually mean by f(x) and g(x) induces same function from F to F?
-the interesting part is the remainder theorem where it says the remainder when f(x) is divided by polynomial (x-a) is f(a) where a is in field F and f(x) is in F[x]. I have solved for remainder many times but have never thought in this way.