Verify if the following polynomials are irreducible over Z3. p(x) = x^3+x+1 p(x)=x^4+1

Verify if the following polynomials are irreducible over Z3.
p(x) = x^3+x+1
p(x)=x^4+1

I am wondering if the following result is correct.
p(x)=x^3+x+1 is irreducible over Z3 because:
p(0)=0+0+1=1 = 1 over Z3.
p(1)=1+1+1=3 = 1 over Z3.
p(2)=8+2+1=11 = 1 over Z3.

p(x)=x^4+1 is not irreducible over Z3 because:
p(1)=1+1=2 = 0 over Z3.