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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
how does the planets on our solar system orbit
how many Messier objects are there in space
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
Roaul
I want to be an astronomer. That's my dream
Astrit
Who named the the whole galaxy?
what is the dark matter
Richard
what are the factors upon which the atmosphere is stratified
bigbang is the beginning of the universe
Sokak
but thats just a theory
Sokak
nothing will happen, don't worry brother.
Vansh
these are Rocky substances between mars and jupiter
GANGAIN
Comets are cosmic snowballs of frozen gases , rock and dust that orbit the sun. They are mostly found between the orbits of Venus and Mercury.
Aarya
hey can anyone guide me abt international astronomy olympiad
sahil
how can we learn right and true ?
why the moon is always appear in an elliptical shape
Because when astroid hit the Earth then a piece of elliptical shape of the earth was separated which is now called moon.
Hemen
Did you mean eye sight or sea level
Minal
oh sorry it's sea level
lidiya
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
w astronomy and cosmology!
Michele
another theory of universe except big ban
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
I think it couldn't possible on earth
Nagalakshmi
in this time i don't Know
Michele
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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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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