Hello

I was hoping someone could tell me which of these two answers are correct.

Question:

Multiply the following polynomials:

(x^7 + x^5 + x^3 + x) * (x^27 + x^15 + x^13 + x^12 + x^11 + 1)

The answer:

x^34 + x^32 + x^30 + x^28 + x^22 + 2x^20 + x^19 + 3x^18 + x^17 + 3x^16 + x^15 + 2x^14 + x^13 + x^12 + x^7 + x^5 + x^3 + x

Now, let's say I want to reduce this modulo 2. Should it become -

A: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

or

B: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^17 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

I think perhaps it should become A, as 3 modulo 2 is 1.

What do you think?

Thank you