# Thread: Polynomials in integer rings

1. ## Polynomials in integer rings

2. For #2 a polynomial of degree less than 5 is written as $\displaystyle a+bx+cx^2+dx^3$ where $\displaystyle a,b,c,d\in \mathbb{Z}_2$. For each $\displaystyle a,b,c,d$ we have two choices either 0 or 1 since we are working in $\displaystyle \mathbb{Z}_2[x]$. Therefore, there are $\displaystyle 2^4 = 16$ such polynomials. For #3 do you know how to apply the division algorithm?

EDIT: Error! It should have been $\displaystyle a+bx+cx^2+dx^3+ex^5$ and in that case we have $\displaystyle 2^5 =32$.

3. There are actually $\displaystyle 2^5=32$ polynomials of degree less than 5.

4. For exercice #3, do a division. Method is the same as with integers.

5. Originally Posted by ThePerfectHacker

EDIT: Error! It should have been $\displaystyle a+bx+cx^2+dx^3+ex^5$ and in that case we have $\displaystyle 2^5 =32$.
I presume you meant ex^4?

Thanks for the help, will get back to you on q3, too early atm and I have a linear alegebra test soon

6. Done the division, worked great, many thanks.