Here is an excerpt from Andrew S. Tanenbaum, Computer Networks, 5th edition, Chapter 3 (The data link layer), Page 213:
When the polynomial code method is employed, the sender and receiver must agree upon a generator polynomial, $G(x)$, in advance. Both the high- and low-order bits of the generator must be 1. To compute the CRC for some frame with $m$ bits corresponding to the polynomial $M(x)$, the frame must be longer than the generator polynomial. The idea is to append a CRC to the end of the frame in such a way that the polynomial represented by the checksummed frame is divisible by $G(x)$. When the receiver gets the checksummed frame, it tries dividing it by $G(x)$. If there is a remainder, there has been a transmission error.
My question is how do you determine high order bit? And why high order bit and lower order bit, both must be one? From my understanding, it is used to detect burst error but is my understanding true?