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To find a possible formula for the polynomial \( P(x) \) given the conditions:

1. **Degree of Polynomial:** 5
2. **Leading Coefficient:** 1
3. **Roots and Multiplicities:**
   - A root of multiplicity 2 at \( x = 3 \)
   - A root of multiplicity 2 at \( x = 0 \)
   - A root of multiplicity 1 at \( x = -4 \)

Given these conditions, we can construct \( P(x) \) as follows:

Since the root at \( x = 3 \) has multiplicity 2, we include \( (x - 3)^2 \) in the expression. Similarly, for the root at \( x = 0 \) with multiplicity 2, we include \( x^2 \). For the root at \( x = -4 \) with multiplicity 1, we include \( (x + 4) \).

Thus, the polynomial \( P(x) \) can be written as:

\[
P(x) = 1 \cdot (x - 3)^2 \cdot x^2 \cdot (x + 4

The polynomial of degree 5, \( P(x) \), has leading coefficient 1, has roots of multiplicity 2 at \( x = 3 \) and \( x = 0 \), and a root of multiplicity 1 at \( x = -4 \). Find a possible formula for \( P(x) \).

Learn how to construct a polynomial of degree 5 with specified roots and multiplicities. This example walks through creating \( P(x) = (x - 3)^2 \cdot x^2 \cdot (x + 4) \), given roots at \( x = 3 \), \( x = 0 \), and \( x = -4 \). Suitable for high school students studying polynomial functions.

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