CRC Polynomial

[dila]

I understand that the CRC is calculated by dividing the message by the CRC polynomial, and the checksum is the remainder of this division.

My question is, if the polynomial is, for example:

x^26 + x^23 + x^22 + x^16 + x^12 + x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x^2 + x + 1

Then why would my checksum ever have the top 5 bits set, because surely the remainder must be strictly less than the modulus?