Answer:
If 1, -5, and -1/2 are zeros of a polynomial function, then the factors of the polynomial are:
(x - 1), (x + 5), and (2x + 1)
To find the polynomial function, we multiply these factors together and simplify:
(x - 1)(x + 5)(2x + 1)
= (x^2 + 4x - 5)(2x + 1)
= 2x^3 + 9x^2 - 6x - 5
Therefore, the polynomial function of the least degree with integral coefficients that has the zeros 1, -5, and -1/2 is:
f(x) = 2x^3 + 9x^2 - 6x - 5