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4 x 3 y 5 2 x y 3 is a binomial of degree 8. The degree of the first term is 8.

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3 x + 10 is a binomial of degree 1.

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Linear quadratic cubic

Polynomials of the first degree are called linear polynomials.
Polynomials of the second degree are called quadratic polynomials.
Polynomials of the third degree are called cubic polynomials.
Polynomials of the fourth degree are called fourth degree polynomials.
Polynomials of the n th degree are called n th degree polynomials.
Nonzero constants are polynomials of the 0th degree.

Some examples of these polynomials follow:

4 x 9 is a linear polynomial.

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3 x 2 + 5 x 7 is a quadratic polynomial.

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8 y 2 x 3 is a cubic polynomial.

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16 a 2 32 a 5 64 is a 5th degree polynomial.

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x 12 y 12 is a 12th degree polynomial.

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7 x 5 y 7 z 3 2 x 4 y 7 z + x 3 y 7 is a 15th degree polynomial. The first term is of degree 5 + 7 + 3 = 15 .

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43 is a 0th degree polynomial.

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Classification of polynomial equations

As we know, an equation is composed of two algebraic expressions separated by an equal sign. If the two expressions happen to be polynomial expressions, then we can classify the equation according to its degree. Classification of equations by degree is useful since equations of the same degree have the same type of graph. (We will study graphs of equations in Chapter 6.)

The degree of an equation is the degree of the highest degree expression.

Sample set a

x + 7 = 15 .

This is a linear equation since it is of degree 1, the degree of the expression on the left of the " = " sign.

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5 x 2 + 2 x 7 = 4 is a quadratic equation since it is of degree 2.

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9 x 3 8 = 5 x 2 + 1 is a cubic equation since it is of degree 3. The expression on the left of the " = " sign is of degree 3.

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y 4 x 4 = 0 is a 4th degree equation.

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a 5 3 a 4 = a 3 + 6 a 4 7 is a 5th degree equation.

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y = 2 3 x + 3 is a linear equation.

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y = 3 x 2 1 is a quadratic equation.

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x 2 y 2 4 = 0 is a 4th degree equation. The degree of x 2 y 2 4 is 2 + 2 = 4 .

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Practice set a

Classify the following equations in terms of their degree.

3 x + 6 = 0

first, or linear

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9 x 2 + 5 x 6 = 3

quadratic

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25 y 3 + y = 9 y 2 17 y + 4

cubic

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5 x 7 = 3 x 5 2 x 8 + 11 x 9

eighth degree

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Exercises

For the following problems, classify each polynomial as a monomial, binomial, or trinomial. State the degree of each polynomial and write the numerical coefficient of each term.

5 x + 7

binomial; first (linear); 5 , 7

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4 x 2 + 9

binomial; second (quadratic); 4 , 9

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a 4 + 1

binomial; fourth; 1 , 1

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5 x

monomial; first (linear); 5

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5 x 3 + 2 x + 3

trinomial; third (cubic); 5 , 2 , 3

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41 a 3 + 22 a 2 + a

trinomial; third (cubic); 41 , 22 , 1

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2 c 6 + 0

monomial; sixth; 2

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9 g

monomial; first (linear); 9

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3 y z 6 y + 11

trinomial; second (quadratic); 3 , 6 , 11

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7 a b 2 c 2 + 2 a 2 b 3 c 5 + a 14

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x 4 y 3 z 2 + 9 z

binomial; ninth; 1 , 9

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6 + 3 x 2 y 5 b

binomial; eighth; 6 , 3

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9 + 3 x 2 + 2 x y 6 z 2

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3 x 2 y 0 z 4 + 12 z 3 , y 0

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4 x y 3 z 5 w 0 , w 0

monomial; ninth; 4

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Classify each of the equations for the following problems by degree. If the term linear, quadratic, or cubic applies, state it.

9 z = 12 x 18

linear

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y 5 + y 3 = 3 y 2 + 2

cubic

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x 2 + x 4 = 7 x 2 2 x + 9

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2 y + 5 x 3 + 4 x y = 5 x y + 2 y

quadratic

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8 a + 2 b = 4 b 8

linear

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2 x 5 8 x 2 + 9 x + 4 = 12 x 4 + 3 x 3 + 4 x 2 + 1

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x + 3 x 5 = x + 2 x 5

fifth degree

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3 x 2 y 4 + 2 x 8 y = 14

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10 a 2 b 3 c 6 d 0 e 4 + 27 a 3 b 2 b 4 b 3 b 2 c 5 = 1 , d 0

19th degree

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The expression 4 x 3 9 x 7 is not a polynomial because

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The expression a 4 7 a is not a polynomial because

. . . there is a variable in the denominator

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Is every algebraic expression a polynomial expression? If not, give an example of an algebraic expression that is not a polynomial expression.

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Is every polynomial expression an algebraic expression? If not, give an example of a polynomial expression that is not an algebraic expression.

yes

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How do we find the degree of a term that contains more than one variable?

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Exercises for review

( [link] ) Use algebraic notation to write “eleven minus three times a number is five.”

11 3 x = 5

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( [link] ) Simplify ( x 4 y 2 z 3 ) 5 .

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( [link] ) Find the value of z if z = x u s and x = 55 , u = 49 , and s = 3 .

z = 2

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( [link] ) List, if any should appear, the common factors in the expression 3 x 4 + 6 x 3 18 x 2 .

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( [link] ) State (by writing it) the relationship being expressed by the equation y = 3 x + 5 .

The value of y is 5 more then three times the value of  x .

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Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
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Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
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faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
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Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
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I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
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ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
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skin
Asiina
skin,Oral,Nasal,GIt
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all
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by fussion
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part of a tissue or an organ being wounded or bruised.
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Binomial nomenclature
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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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