# monic polynomials

• Oct 18th 2008, 07:21 AM
knguyen2005
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
• Oct 18th 2008, 08:01 AM
Moo
Hello,
Quote:

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 \$\displaystyle 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.
• Oct 18th 2008, 03:57 PM
ThePerfectHacker
Quote:

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.