# Math Help - monic polynomials

1. ## monic polynomials

Can somebody give me hints on these question please?

(i) List all the monic polynomials over
F2 of degree =<3.
(ii) Determine which of these polynomials are irreducible over
F2.

(iii) Factorize the reducible polynomials into irreducible polynomials.

Thanks alot

2. Hello,
Originally Posted by knguyen2005
Can somebody give me hints on these question please?

(i) List all the monic polynomials over F2 of degree =<3.
(ii) Determine which of these polynomials are irreducible over F2.
(iii) Factorize the reducible polynomials into irreducible polynomials.

Thanks alot
i) In $F_2$ the possible coefficients are 0 and 1.
ii) list them first, then try to see if they can be factored...
iii) ... if they can, factor them.

3. Originally Posted by Moo
ii) list them first, then try to see if they can be factored...
I want to add something to Moo, angle.

Those polynomials are factorable if and only if they have zeros.