Math Problem Statement

Give the degree of the polynomial: 6y^8 + 9v^4 y^2 x - 6 + x^4 v^2

Solution

To determine the degree of the given polynomial, we need to find the highest sum of exponents of the variables in any term of the polynomial. Let's examine the polynomial:

6y8+9v4y2x6+x4v26y^8 + 9v^4 y^2 x - 6 + x^4 v^2

Now, we'll look at each term:

  1. 6y86y^8: The degree is 8 (since the exponent of yy is 8).
  2. 9v4y2x9v^4 y^2 x: The degree is 4+2+1=74 + 2 + 1 = 7 (summing the exponents of vv, yy, and xx).
  3. 6-6: This is a constant term, so the degree is 0.
  4. x4v2x^4 v^2: The degree is 4+2=64 + 2 = 6 (summing the exponents of xx and vv).

The highest degree among these terms is 8 (from 6y86y^8).

Thus, the degree of the polynomial is 8.

Would you like further details or explanations on any part of this?

Here are 5 related questions to deepen your understanding:

  1. How do you determine the degree of a term with multiple variables?
  2. What is the degree of a constant polynomial?
  3. Can a polynomial have more than one term with the highest degree?
  4. How does the degree of a polynomial affect its graph?
  5. What is the difference between the degree of a term and the degree of a polynomial?

Tip: The degree of a polynomial gives an idea of the highest power of the variable(s) involved, which also indicates the potential complexity of its graph!

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Math Problem Analysis

Mathematical Concepts

Polynomial Degree
Algebra

Formulas

Degree of a term = sum of exponents of variables in the term

Theorems

The degree of a polynomial is the highest degree of any of its terms

Suitable Grade Level

Grades 8-10