Let's analyze the given function $f(x) = -(x + 1)^3 (x - 1)^2$ and its graph.

Degree of the Polynomial:

To determine the degree of a polynomial, we add the exponents of each factor.

• The factor $(x + 1)^3$ has an exponent of 3.
• The factor $(x - 1)^2$ has an exponent of 2.

Adding these exponents gives $3 + 2 = 5$.

Thus, the degree of the polynomial is 5.

Would you like further explanation on any specific part of this? Here are some related questions:

1. How does the degree of a polynomial affect the shape of the graph?
2. What is the significance of the leading coefficient being negative?
3. How do the multiplicities of the zeros affect the graph’s behavior at each intercept?
4. How can we use the polynomial's factored form to determine end behavior?
5. What would the graph look like if the degree were even instead of odd?

Tip: The degree of a polynomial also dictates the maximum number of turning points it can have. A degree 5 polynomial can have up to 4 turning points.