Prove Corollary 1 and 2 of Theorem 16.2. Corollary 1 of Theorem 16.2 states: Let F be a field, a ∈ F, and f(x) ∈ F[x]. Then f(a) is the remainder in the division of f(x) by x – a. Corollary 2 of Theorem 16.2 states: Let F be a field, a ∈ F, and f(x) ∈ F[x]. Then a is a zero of f(x) if and only if  x – a is a factor of f(x). Contemporary Abstract Algebra

Prove Corollary 1 and 2 of Theorem 16.2.

Corollary 1 of Theorem 16.2 states: Let F be a field, a ∈ F, and f(x) ∈ F[x]. Then f(a) is the remainder in the division of f(x) by x – a.

Corollary 2 of Theorem 16.2 states: Let F be a field, a ∈ F, and f(x) ∈ F[x]. Then a is a zero of f(x) if and only if  x – a is a factor of f(x).

Contemporary Abstract Algebra