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What is the polynomial function of the least degree that has -2, 3, and 4 as its only zeros? Could you please explain the process for finding it?

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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:

  1. Write each zero as a factor set to zero: x = -2, x = 3, x = 4.
  2. Convert these into the corresponding factors: (x + 2), (x - 3), (x - 4).
  3. Multiply the factors together to get the polynomial: (x + 2)(x - 3)(x - 4).
  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.

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