Answer:
A third-degree polynomial function in factored form is typically expressed as f(x) = a(x - r)(x - s)(x - t), where r, s, and t are the zeros of the function and a is the leading coefficient.
Given the zeros of the function are -5, -1, and 2, and the leading coefficient a is 1/2, we can substitute these values into the formula to find the polynomial function in factored form:
f(x) = 1/2(x - (-5))(x - (-1))(x - 2)
Therefore, the polynomial function in factored form is:
f(x) = 1/2(x + 5)(x + 1)(x - 2)