Mark each of the following true or false. 

___ a. x - 2 is irreducible over Q. 

___ b. 3x - 6 is irreducible over Q. 

___ c. x² - 3 is irreducible over Q. 

___ d. x² + 3 is irreducible over Z₇. 

___ e. If F is a field, the units of F[x] are precisely the nonzero elements of F. 

___ f. If F is a field, the units of F[x] are precisely the nonzero elements of F. 

___ g. A polynomial f (x) of degree n with coefficients in a field F can have at most n zeros in F. 

___ h. A polynomial f (x) of degree n with coefficients in a field F can have at most n zeros in any given field E such that F ≤ E. 

___ i. Every polynomial of degree 1 in F[x] has at least one zero in the field F. 

___ j. Each polynomial in F[x] can have at most a finite number of zeros in the field F.