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- Classification of expressions
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: be familar with polynomials, be able classify polynomials and polynomial equations.
Overview
- Polynomials
- Classification of Polynomials
- Classification of Polynomial Equations
Polynomials
Polynomials
Let us consider the collection of all algebraic expressions that do not contain variables in the denominators of fractions and where all exponents on the variable quantities are whole numbers. Expressions in this collection are called
polynomials.
Some expressions that
are polynomials are
Some expressions that
are not polynomials are
Classification of polynomials
Polynomials can be classified using two criteria: the number of terms and degree of the polynomial.
Number of Terms |
Name |
Example |
Comment |
One |
Monomial |
|
mono means “one” in Greek. |
Two |
Binomial |
|
bi means “two” in Latin. |
Three |
Trinomial |
|
tri means “three” in Greek. |
Four or more |
Polynomial |
|
poly means “many” in Greek. |
Degree of a term containing one variable
The
degree of a term containing only
one variable is the value of the exponent of the variable. Exponents appearing on numbers do not affect the degree of the term. We consider only the exponent of the variable. For example:
8 is a monomial of degree 0. We say that a nonzero number is a term of 0 degree since it could be written as
. Since
,
. The exponent on the variable is 0 so it must be of degree 0. (By convention, the number 0 has no degree.)
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Degree of a term containing several variables
The degree of a term containing
more than one variable is the
sum of the exponents of the variables, as shown below.
Degree of a polynomial
The
degree of a polynomial is the degree of the
term of highest degree; for example:
is a trinomial of degree 3. The first term,
, is the term of the highest degree. Therefore, its degree is the degree of the polynomial.
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Questions & Answers
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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