To solve each of these questions, let's go through them one by one, focusing on the degree of each term and the polynomial.

1. Find the degree of the term $3x^6$:

• The degree of a term with one variable is the exponent of the variable. Here, the exponent of $x$ is 6.
• Answer: The degree of $3x^6$ is 6.

2. Find the degree of the term $-4$:

• The term $-4$ is a constant, and constants have a degree of 0.
• Answer: The degree of $-4$ is 0.

3. Find the degree of the term $-5x^9$:

• The exponent of $x$ in $-5x^9$ is 9.
• Answer: The degree of $-5x^9$ is 9.

4. Find the degree of the term $4x^8$:

• The exponent of $x$ in $4x^8$ is 8.
• Answer: The degree of $4x^8$ is 8.

5. Find the degree of the polynomial $3x^6 - 4 - 5x^9 + 4x^8$:

• The degree of a polynomial is the highest degree of any individual term within it.
• The degrees of the terms are:
  • $3x^6$: 6
  • $-4$: 0
  • $-5x^9$: 9
  • $4x^8$: 8
• The highest degree among these terms is 9.
• Answer: The degree of the polynomial $3x^6 - 4 - 5x^9 + 4x^8$ is 9.

Let me know if you'd like more details or have questions on any step.

Related Questions:

1. What is the degree of a polynomial with terms that all have the same degree?
2. How does the degree of a constant term compare to variable terms?
3. How do we determine the degree of a polynomial with multiple variables?
4. Why is the degree of a constant term always 0?
5. What is the effect of adding or subtracting terms on the degree of a polynomial?

Tip:

The degree of a polynomial is always determined by the term with the highest power of the variable, even if it's negative or involves a coefficient.