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!

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.