Math Problem Statement

Find the degree of the term 2x^5, Find the degree of the term 1x^3, Find the degree of the term 3x^6, Find the degree of the term 5, Find the degree of the polynomial 2x^5 + 1x^3 + 3x^6 + 5.

Solution

Let's go through each part of the problem:

  1. Degree of the term 2x52x^5:

    • The degree of a term is the exponent of the variable.
    • For 2x52x^5, the exponent of xx is 5.
    • Answer: 5
  2. Degree of the term 1x31x^3:

    • The exponent of xx is 3.
    • Answer: 3
  3. Degree of the term 3x63x^6:

    • The exponent of xx is 6.
    • Answer: 6
  4. Degree of the term 55:

    • This is a constant term (there's no variable). The degree of a constant is 0.
    • Answer: 0
  5. Degree of the polynomial 2x5+1x3+3x6+52x^5 + 1x^3 + 3x^6 + 5:

    • The degree of a polynomial is the highest degree of its terms.
    • The highest exponent among the terms is 6 (from 3x63x^6).
    • Answer: 6

Would you like further details on this solution?

Here are 5 related questions for practice:

  1. What is the degree of the term 4x7-4x^7?
  2. What is the degree of the polynomial 4x2+9x+74x^2 + 9x + 7?
  3. What is the degree of a constant term, like 8-8?
  4. How would the degree change if there are multiple variables, e.g., 5x2y35x^2y^3?
  5. What is the degree of the polynomial 7x43x2+27x^4 - 3x^2 + 2?

Tip: The degree of a polynomial helps in understanding its behavior for large values of xx, as the highest degree term dominates.

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Math Problem Analysis

Mathematical Concepts

Polynomials
Degree of a term

Formulas

Degree of a term is the exponent of the variable
Degree of a polynomial is the highest degree among its terms

Theorems

Fundamental understanding of polynomial degrees

Suitable Grade Level

Grades 6-8