Math Problem Statement

Find the degrees of individual terms and the polynomial: 3x^6, -4, -5x^9, 4x^8, and 3x^6 - 4 - 5x^9 + 4x^8.

Solution

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 3x63x^6:

  • The degree of a term with one variable is the exponent of the variable. Here, the exponent of xx is 6.
  • Answer: The degree of 3x63x^6 is 6.

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

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

3. Find the degree of the term 5x9-5x^9:

  • The exponent of xx in 5x9-5x^9 is 9.
  • Answer: The degree of 5x9-5x^9 is 9.

4. Find the degree of the term 4x84x^8:

  • The exponent of xx in 4x84x^8 is 8.
  • Answer: The degree of 4x84x^8 is 8.

5. Find the degree of the polynomial 3x645x9+4x83x^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:
    • 3x63x^6: 6
    • 4-4: 0
    • 5x9-5x^9: 9
    • 4x84x^8: 8
  • The highest degree among these terms is 9.
  • Answer: The degree of the polynomial 3x645x9+4x83x^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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Degree
Exponent

Formulas

Degree of a term with a variable: exponent of the variable
Degree of a constant term is always 0
Degree of a polynomial is the highest degree of its terms

Theorems

Definition of polynomial degree

Suitable Grade Level

Grades 7-9