To determine the degree of the polynomial $f(x) = -x^3 + 5x^2 + 6x + 1$, we identify the highest power of $x$ in the polynomial.

Solution:

• The polynomial $f(x) = -x^3 + 5x^2 + 6x + 1$ contains terms with powers of $x$: $3$, $2$, $1$, and $0$.
• The highest power is $3$, which comes from the term $-x^3$.

Final Answer:

The degree of $f(x)$ is 3.

Would you like a further explanation or have any follow-up questions?

Here are 5 related questions you might find helpful:

1. What is the degree of the polynomial $4x^5 - 3x^2 + 7$?
2. How do you determine the degree of a polynomial?
3. Can the degree of a polynomial be negative?
4. What happens to the degree if two polynomials are added or multiplied?
5. How does the degree of a polynomial relate to its graph?

Tip: The degree of a polynomial helps determine its general shape and the number of roots it may have.