<< Chapter < Page Chapter >> Page >

5 x 3 ( y 7 ) means there are five x 3 ( y 7 ) ' s . It could also mean there are 5 x 3 ( x 7 ) ' s . It could also mean there are 5 ( x 7 ) x 3 ' s .

Got questions? Get instant answers now!

Practice set d

What does the coefficient of a quantity tell us?

The difference between coefficients and exponents

It is important to keep in mind the difference between coefficients and exponents .

Coefficients record the number of like terms in an algebraic expression.
x + x + x + x 4 terms = 4 x coefficient is 4
Exponents record the number of like factors in a term.
x x x x 4 factors = x 4 exponent is 4

In a term, the coefficient of a particular group of factors is the remaining group of factors.

how many of that quantity there are

Got questions? Get instant answers now!

Sample set e

3 x .

The coefficient of x is 3.

Got questions? Get instant answers now!

6 a 3 .

The coefficient of a 3 is 6.

Got questions? Get instant answers now!

9 ( 4 a ) .

The coefficient of ( 4 a ) is 9.

Got questions? Get instant answers now!

3 8 x y 4 .

The coefficient of x y 4 is 3 8 .

Got questions? Get instant answers now!

3 x 2 y .

The coefficient of x 2 y is 3; the coefficient of y is 3 x 2 ; and the coefficient of 3 is x 2 y .

Got questions? Get instant answers now!

4 ( x + y ) 2 .

The coefficient of ( x + y ) 2 is 4; the coefficient of 4 is ( x + y ) 2 ; and the coefficient of ( x + y ) is 4 ( x + y ) since 4 ( x + y ) 2 can be written as 4 ( x + y ) ( x + y ) .

Got questions? Get instant answers now!

Practice set e

Determine the coefficients.
In the term 6 x 3 , the coefficient of
(a) x 3 is .
(b) 6 is .

(a) 6 (b) x 3

Got questions? Get instant answers now!

In the term 3 x ( y 1 ) , the coefficient of
(a) x ( y 1 ) is .
(b) ( y 1 ) is .
(c) 3 ( y 1 ) is .
(d) x is .
(e) 3 is .
(f) The numerical coefficient is .

(a) 3 (b) 3 x (c) x (d) 3 ( y 1 ) (e) x ( y 1 ) (f) 3

Got questions? Get instant answers now!

In the term 10 a b 4 , the coefficient of
(a) a b 4 is .
(b) b 4 is .
(c) a is .
(d) 10 is .
(e) 10 a b 3 is .

(a) 10 (b) 10 a (c) 10 b 4 (d) a b 4 (e) b

Got questions? Get instant answers now!

Exercises

What is an algebraic expression?

An algebraic expression is a number, a letter, or a collection of numbers and letters along with meaningful signs of operation.

Got questions? Get instant answers now!

Why is the number 14 considered to be an expression?

Got questions? Get instant answers now!

Why is the number x considered to be an expression?

x is an expression because it is a letter (see the definition).

Got questions? Get instant answers now!

For the expressions in the following problems, write the number of terms that appear and then list the terms.

6 x 10

two : 6 x , 10

Got questions? Get instant answers now!

5 x 2 + 6 x 2

three : 5 x 2 , 6 x , 2

Got questions? Get instant answers now!

5 c z

one : 5 c z

Got questions? Get instant answers now!

4 y 3

one : 4 y 3

Got questions? Get instant answers now!

a + 1

two : a , 1

Got questions? Get instant answers now!

2 x + x + 7

three : 2 x , x , 7

Got questions? Get instant answers now!

( a + 1 ) + ( a 1 )

two : ( a + b ) , ( a 1 )

Got questions? Get instant answers now!

For the following problems, list, if any should appear, the common factors in the expressions.

x 2 + 5 x 2 2 x 2

x 2

Got questions? Get instant answers now!

2 ( a + b ) 3 ( a + b )

( a + b )

Got questions? Get instant answers now!

8 a 2 ( b + 1 ) 10 a 2 ( b + 1 )

Got questions? Get instant answers now!

14 a b 2 c 2 ( c + 8 ) + 12 a b 2 c 2

2 a b 2 c 2

Got questions? Get instant answers now!

9 a ( a 3 ) 2 + 10 b ( a 3 )

( a 3 )

Got questions? Get instant answers now!

12 a 3 b 2 c 7 ( b + 1 ) ( c a )

no commom factors

Got questions? Get instant answers now!

5.2 ( a + 7 ) 2 + 17.1 ( a + 7 )

( a + 7 )

Got questions? Get instant answers now!

3 4 x 2 y 2 z 2 + 3 8 x 2 z 2

Got questions? Get instant answers now!

9 16 ( a 2 b 2 ) + 9 32 ( b 2 a 2 )

9 32

Got questions? Get instant answers now!

For the following problems, note how many:

z ' s in 12 z ?

12

Got questions? Get instant answers now!

x 2 's in 5 x 2 ?

Got questions? Get instant answers now!

y 3 's in 6 y 3 ?

6

Got questions? Get instant answers now!

x y ' s in 9 x y ?

Got questions? Get instant answers now!

a 2 b ' s in 10 a 2 b ?

10

Got questions? Get instant answers now!

( a + 1 ) ' s in 4 ( a + 1 ) ?

Got questions? Get instant answers now!

( 9 + y ) ' s in 8 ( 9 + y ) ?

8

Got questions? Get instant answers now!

y 2 's in 3 x 3 y 2 ?

Got questions? Get instant answers now!

12 x ' s in 12 x 2 y 5 ?

x y 5

Got questions? Get instant answers now!

( a + 5 ) ' s in 2 ( a + 5 ) ?

Got questions? Get instant answers now!

( x y ) ' s in 5 x ( x y ) ?

5 x

Got questions? Get instant answers now!

( x + 1 ) ' s in 8 ( x + 1 ) ?

Got questions? Get instant answers now!

2 ' s in 2 x 2 ( x 7 ) ?

x 2 ( x 7 )

Got questions? Get instant answers now!

3 ( a + 8 ) ' s in 6 x 2 ( a + 8 ) 3 ( a 8 ) ?

Got questions? Get instant answers now!

For the following problems, a term will be given followed by a group of its factors. List the coefficient of the given group of factors.

12 a 2 b 3 c 2 r 7 ; a 2 c 2 r 7

Got questions? Get instant answers now!

6 x 2 b 2 ( c 1 ) ; c 1

6 x 2 b 2

Got questions? Get instant answers now!

10 x ( x + 7 ) 2 ; 10 ( x + 7 )

Got questions? Get instant answers now!

9 a 2 b 5 ; 3 a b 3

3 a b 2

Got questions? Get instant answers now!

15 x 4 y 4 ( z + 9 a ) 3 ; ( z + 9 a )

Got questions? Get instant answers now!

( 4 ) a 6 b 2 ; a b

( 4 ) a 5 b

Got questions? Get instant answers now!

( 11 a ) ( a + 8 ) 3 ( a 1 ) ; ( a + 8 ) 2

Got questions? Get instant answers now!

Exercises for review

( [link] ) Simplify [ 2 x 8 ( x 1 ) 5 x 4 ( x 1 ) 2 ] 4 .

16 x 16 ( x 1 ) 12

Got questions? Get instant answers now!

( [link] ) Supply the missing phrase. Absolute value speaks to the question of and not "which way."

Got questions? Get instant answers now!

( [link] ) Find the value of [ 6 ( 4 2 ) + 7 ( 3 + 5 ) ] .

50

Got questions? Get instant answers now!

( [link] ) Find the value of 2 5 4 2 3 2 .

Got questions? Get instant answers now!

( [link] ) Express 0.0000152 using scientific notation.

1.52 × 10 5

Got questions? Get instant answers now!

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask