Final answer:
The polynomial function of least degree with zeros -4, 2, and 3 is a cubic function given by f(x) = x^3 - x^2 - 10x + 24.
Step-by-step explanation:
We need to find the polynomial function of the least degree that has -4, 2, and 3 as its only zeros. Since these zeros are all distinct, the minimum degree of the polynomial function with these zeros is 3, making it a cubic function. A polynomial of degree 3 has the general form f(x) = ax^3 + bx^2 + cx + d. To construct this polynomial function, we use the zeros in the form (x + 4)(x - 2)(x - 3). Multiplying these factors out, we get:
f(x) = (x + 4)(x - 2)(x - 3) = x^3 - x^2 - 10x + 24
Therefore, the simplest polynomial function with the given zeros is f(x) = x^3 - x^2 - 10x + 24.