Mark each of the following true or false. 

___ a. The polynomial (a_nxⁿ + · · · + a₁x + a₀) ∈ R[x] is 0 if and only if a_i = 0, for i = 0, 1, · · ·, n. 

___ b. If R is a commutative ring, then R[x] is commutative. 

___ c. If D is an integral domain, then D[x] is an integral domain. 

___ d. If R is a ring containing divisors of 0, then R [x] has divisors of 0. 

___ e. If R is a ring and f (x) and g(x) in R [x] are of degrees 3 and 4, respectively, then f (x )g(x) may be of degree 8 in R[x]. 

___ f. If R is any ring and f(x) and g(x) in R[x] are of degrees 3 and 4, respectively, then f(x)g(x) is always of degree 7. 

___ g. If F is a subfield E and α ∈ E is a zero of f(x) ∈ F[x], then α is a zero of h(x) = f(x)g(x) for all g(x)∈ F[x].

___ h. If F is a field, then the units in F[x] are precisely the units in F. 

___ i. If R is a ring, then x is never a divisor of 0 in R [x]. 

___ j. If R is a ring, then the zero divisors in R[x] are precisely the zero divisors in R.