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The trick is first to define the ring where your polynomial will live, namely Polynomial Ring in the undeterminate x over the finite field of size 3, $\mathbf[F}_3[x]$:

sage: R.<x> = GF(3)[]

This defines both R and x:

sage: R
Univariate Polynomial Ring in x over Finite Field of size 3

sage: x
x
sage: x.parent()
Univariate Polynomial Ring in x over Finite Field of size 3

Then, you can do:

sage: P = x^8+x^2+1
sage: P.is_irreducible()
False

sage: P.factor()
(x + 1) * (x + 2) * (x^3 + 2*x + 1) * (x^3 + 2*x + 2)

The trick is first to define the ring where your polynomial will live, namely Polynomial Ring in the undeterminate x over the finite field of size 3, $\mathbf[F}_3[x]$:$\mathbf{F}_3[x]$:

sage: R.<x> = GF(3)[]

This defines both R and x:

sage: R
Univariate Polynomial Ring in x over Finite Field of size 3

sage: x
x
sage: x.parent()
Univariate Polynomial Ring in x over Finite Field of size 3

Then, you can do:

sage: P = x^8+x^2+1
sage: P.is_irreducible()
False

sage: P.factor()
(x + 1) * (x + 2) * (x^3 + 2*x + 1) * (x^3 + 2*x + 2)

The trick is first to define the ring R where your polynomial will live, namely Polynomial Ring in the undeterminate x over the finite field of size 3, $\mathbf{F}_3[x]$:

sage: R.<x> = GF(3)[]

This defines both R and x:

sage: R
Univariate Polynomial Ring in x over Finite Field of size 3

sage: x
x
sage: x.parent()
Univariate Polynomial Ring in x over Finite Field of size 3

Then, you can do:

sage: P = x^8+x^2+1
sage: P.is_irreducible()
False

sage: P.factor()
(x + 1) * (x + 2) * (x^3 + 2*x + 1) * (x^3 + 2*x + 2)