Final answer:
The correct factored form for g(x), which has roots -1, 1, and 2, is g(x) = (x + 1) (x - 1) (x - 2), and since 2 is a root, g(2) is equal to 0 in any form.
Step-by-step explanation:
If g(x) is a polynomial that has roots -1, 1, and 2, then the factored form of g(x) will reflect these roots as (x + 1), (x - 1), and (x - 2), respectively. The correct factored form for g(x) is therefore g(x) = (x + 1) (x - 1) (x - 2). This polynomial is a product of linear factors, each factor corresponding to one of the given roots.
When you want to find the value of g(2), you substitute x with 2 in the polynomial function. However, since we know that 2 is a root of the polynomial g(x), by the definition of a root, g(2) must be 0. As a result, in factored form, g(2) remains 0 and is not affected by the particular factors of the polynomial.