Degree and descending powers
Degree and Descending Powers introduces the vocabulary and conventions for polynomials: the degree of a term is the exponent of its variable, and the degree of a polynomial is the highest exponent. Covered in Yoshiwara Elementary Algebra Chapter 7: Polynomials, this concept teaches Grade 6 students to write polynomials in standard form (descending powers), where terms are arranged from highest to lowest degree. Understanding degree helps classify polynomials and anticipate their graphical behavior.
Key Concepts
Property In a term containing only one variable, the exponent of the variable is called the degree of the term. The degree of a polynomial in one variable is the largest exponent that appears in any term. Polynomials in one variable are usually written in descending powers of the variable.
Examples The polynomial $3y^2 2y + 2$ has a degree of 2.
The polynomial $m 2m^2 + m^5$ has a degree of 5.
Common Questions
What is the degree of a polynomial?
The degree of a polynomial is the largest exponent that appears among all its terms. For example, 3x⁴ + 2x² - 5 has degree 4.
What does writing in descending powers mean?
Descending powers means arranging the terms of a polynomial from highest exponent to lowest: for example, 5x³ - 2x² + x - 7.
What is the degree of a constant term?
A nonzero constant has degree 0, because x⁰ = 1. The number 7 can be written as 7x⁰.
Where is degree and descending powers in Yoshiwara Elementary Algebra?
This vocabulary is introduced in Chapter 7: Polynomials of Yoshiwara Elementary Algebra.
Why do we write polynomials in descending order?
Descending order is the standard form that makes it easier to identify the degree, compare polynomials, and perform operations like addition and division.