Make a list of all irreducible polynomials of degrees 1 to 5 over F2

[Hill]

TL;DR Summary

F2 = (0, 1)

To this exercise,

the textbook's solution is

I didn't follow their method and have found another degree 5 solution, $X^5+X^4+X^2+X+1$.
Is it wrong or the book has omitted this solution?

 

[martinbn]

TL;DR Summary: F2 = (0, 1)

To this exercise,
View attachment 355323
the textbook's solution is
View attachment 355324
I didn't follow their method and have found another degree 5 solution, $X^5+X^4+X^2+X+1$.
Is it wrong or the book has omitted this solution?

It is irreducible. I guess they missed it.

 

[Hill]

It is irreducible. I guess they missed it.

As well as
$X^5+X^4+X^3+X+1$
$X^5+X^3+X^2+X+1$
$X^5+X^4+X^3+X^2+1$
(?)