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The problem asks for the polynomial function of the least degree whose only zeros are \( -2 \), \( 3 \), and \( 4 \). Based on the given options, the structure of the polynomial will be:

\[
f(x) = a(x + 2)(x - 3)(x - 4)
\]

Since the leading term is given as \( x^3 \), the constant \( a \) should be 1 (since the highest degree term \( x^3 \) already matches). Expanding the factors:

\[
(x + 2)(x - 3)(x - 4)
\]

First, multiply the first two factors:

\[
(x + 2)(x - 3) = x^2 - 3x + 2x - 6 = x^2 - x - 6
\]

Now, multiply this result by \( (x - 4) \):

\[
(x^2 - x - 6)(x - 4) = x^3 - 4x^2 - x^2 + 4x - 6x + 24
\]

Simplify the terms:

\[
x^3 - 5x^2 + 10x + 24
\]

Thus, the polynomial is:

\[
f(x) = x^3 - 5x^2 + 10x + 24
\]

The corresponding values to drag into the boxes are:

- For \( x^2 \), the coefficient is \( -5 \),
- For \( x \), the coefficient is \( +10 \),
- For the constant term, the value is \( +24 \).

Let me know if you'd like further details or clarifications!

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Here are 5 related questions:
1. What would the polynomial look like if the zeros were \( 1 \), \( -3 \), and \( 5 \)?
2. How do you determine the leading coefficient in a polynomial?
3. What are the possible degrees for a polynomial with 4 real zeros?
4. How can you verify the zeros of a polynomial by factoring?
5. How does the degree of a polynomial affect its end behavior?

**Tip:** When finding the polynomial from given zeros, always check for the highest-degree term to match the expected degree of the polynomial.

What is the polynomial function of least degree whose only zeros are −2, 3, and 4?

Explore how to construct a polynomial function with specified zeros at -2, 3, and 4. This guide provides a step-by-step solution for forming and expanding the polynomial, suitable for high school level students.

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