degree of a term

Thân thiện

A student writes the degree of a term on a chalkboard.

Definition

1. Noun:
   • The sum of the exponents of the variables in a term: In algebra, the "degree of a term" is a numerical value calculated by adding together all the exponents of the variables present in a single term. For a term with only one variable, it is simply the exponent of that variable. For a constant term (a term with no variables), the degree is 0.

Usage

• The "degree of a term" is a fundamental concept used to classify and organize algebraic expressions, particularly polynomials.
• It is used to determine the overall degree of a polynomial, which is the highest degree among all its terms.
• Understanding the degree helps in operations like addition, multiplication, and factoring of polynomials.

Examples

• Noun:
  • In the term 5x³, the degree of the term is 3.
  • In the term -2x²y⁴, the degree of the term is 2 + 4 = 6.
  • For the constant term 7, the degree of the term is 0.
  • To find the degree of the polynomial 3x⁵ + x²y - 4, you must first find the degree of each term.

Advanced Usage

• "Degree of a term in multiple variables": When a term contains more than one variable, you sum the exponents of all variables. For example, in , the degree is 1+2+3=6.
• "Leading term": In a polynomial, the term with the highest degree is often called the leading term. Identifying it requires calculating the degree of each term.

Variants and Related Words

• Degree of a polynomial (n): The highest degree among all the terms in a polynomial.
  • The degree of the polynomial x³ + 2x + 1 is 3.
• Monomial (n): An algebraic expression consisting of only one term. The degree of a term is directly the degree of a monomial.
  • 4a²b is a monomial of degree 3.

Synonyms

• Term degree: A less common but equivalent phrase.
• Total degree: Often used interchangeably, especially for terms with multiple variables.

Related Phrases

• "Find the degree of...": A common instructional phrase in algebra.
  • The first step is to find the degree of each term in the expression.
• "Term of degree n": A way to describe a term based on its calculated degree.
  • xy² is a term of degree 3.

Notes

• The degree of a term is always a non-negative integer.
• For a term like (where the exponent is 1), the degree is 1.
• The concept is specific to terms within polynomials and other algebraic expressions.

Học thuật

Noun

1. the sum of the exponents of the variables in the term