Answer:
The polynomial function is f(x) = 3(x+4)(x-i)(x+2).
Step-by-step explanation:
The problem can be solved by elimination. In this case the correct answer is the first, so our search is short.
First, notice that the polynomial function given by f(x) = 3(x+4)(x-i)(x+2) has exactly three roots, in fact, those roots are -4, i and 2 as the statement of the exercise asks. Moreover, as all the factors (x+4)(x-i)(x+2) have leading coefficient 1, their product will have leading coefficient 1. Then, as 3 is multiplying x+4)(x-i)(x+2), the leading coefficient of f(x) is 3.
The other three cases do not satisfy the conditions of the exercise because of all of them have more roots than -4, i and 2.
