The main result is that if is a non-constant polynomial in there exists an extension field such that there is so that . Given a non-constant polynomial of degree you can construct so that is an extension field that with . Think of as a polynomial in since it has as a zero it means where . But that means there is a field so that and there is with . And so this means if viewed as a polynomial in . Continuing in this way we can construct, so that the entire polynomial (which has degree ) can be written into linear factors over .