Final answer:
The polynomial function of least degree with zeros -2, 3, and 4 is obtained by converting each zero into a factor and multiplying them together, resulting in the function x^3 - 5x^2 - 2x + 24.
Step-by-step explanation:
The polynomial function of the least degree that has -2, 3, and 4 as its only zeros is obtained by writing a polynomial where each zero is represented as a factor. Since the zeros are -2, 3, and 4, the corresponding factors are (x + 2), (x - 3), and (x - 4). The polynomial of least degree containing these factors is found by multiplying them together.
To find this polynomial, we follow these steps:
- Write each zero as a factor set to zero: x = -2, x = 3, x = 4.
- Convert these into the corresponding factors: (x + 2), (x - 3), (x - 4).
- Multiply the factors together to get the polynomial: (x + 2)(x - 3)(x - 4).
- Simplify the multiplication to get the polynomial in standard form.
After simplifying, the polynomial function is: x^3 - 5x^2 - 2x + 24.
This third-degree polynomial is the simplest polynomial that has the given zeros.