<< Chapter < Page Chapter >> Page >

Section exercises

Verbal

If division of a polynomial by a binomial results in a remainder of zero, what can be conclude?

The binomial is a factor of the polynomial.

Got questions? Get instant answers now!

If a polynomial of degree n is divided by a binomial of degree 1, what is the degree of the quotient?

Got questions? Get instant answers now!

Algebraic

For the following exercises, use long division to divide. Specify the quotient and the remainder.

( x 2 + 5 x 1 ) ÷ ( x 1 )

x + 6 + 5 x - 1 , quotient: x + 6 , remainder: 5

Got questions? Get instant answers now!

( 2 x 2 9 x 5 ) ÷ ( x 5 )

Got questions? Get instant answers now!

( 3 x 2 + 23 x + 14 ) ÷ ( x + 7 )

3 x + 2 , quotient:  3 x + 2 , remainder: 0

Got questions? Get instant answers now!

( 4 x 2 10 x + 6 ) ÷ ( 4 x + 2 )

Got questions? Get instant answers now!

( 6 x 2 25 x 25 ) ÷ ( 6 x + 5 )

x 5 , quotient: x 5 , remainder: 0

Got questions? Get instant answers now!

( x 2 1 ) ÷ ( x + 1 )

Got questions? Get instant answers now!

( 2 x 2 3 x + 2 ) ÷ ( x + 2 )

2 x 7 + 16 x + 2 , quotient: 2 x 7 , remainder: 16

Got questions? Get instant answers now!

( x 3 126 ) ÷ ( x 5 )

Got questions? Get instant answers now!

( 3 x 2 5 x + 4 ) ÷ ( 3 x + 1 )

x 2 + 6 3 x + 1 , quotient: x 2 , remainder: 6

Got questions? Get instant answers now!

( x 3 3 x 2 + 5 x 6 ) ÷ ( x 2 )

Got questions? Get instant answers now!

( 2 x 3 + 3 x 2 4 x + 15 ) ÷ ( x + 3 )

2 x 2 3 x + 5 , quotient: 2 x 2 3 x + 5 , remainder: 0

Got questions? Get instant answers now!

For the following exercises, use synthetic division to find the quotient.

( 3 x 3 2 x 2 + x 4 ) ÷ ( x + 3 )

Got questions? Get instant answers now!

( 2 x 3 6 x 2 7 x + 6 ) ÷ ( x 4 )

2 x 2 + 2 x + 1 + 10 x 4

Got questions? Get instant answers now!

( 6 x 3 10 x 2 7 x 15 ) ÷ ( x + 1 )

Got questions? Get instant answers now!

( 4 x 3 12 x 2 5 x 1 ) ÷ ( 2 x + 1 )

2 x 2 7 x + 1 2 2 x + 1

Got questions? Get instant answers now!

( 9 x 3 9 x 2 + 18 x + 5 ) ÷ ( 3 x 1 )

Got questions? Get instant answers now!

( 3 x 3 2 x 2 + x 4 ) ÷ ( x + 3 )

3 x 2 11 x + 34 106 x + 3

Got questions? Get instant answers now!

( 6 x 3 + x 2 4 ) ÷ ( 2 x 3 )

Got questions? Get instant answers now!

( 2 x 3 + 7 x 2 13 x 3 ) ÷ ( 2 x 3 )

x 2 + 5 x + 1

Got questions? Get instant answers now!

( 3 x 3 5 x 2 + 2 x + 3 ) ÷ ( x + 2 )

Got questions? Get instant answers now!

( 4 x 3 5 x 2 + 13 ) ÷ ( x + 4 )

4 x 2 21 x + 84 323 x + 4

Got questions? Get instant answers now!

( x 3 3 x + 2 ) ÷ ( x + 2 )

Got questions? Get instant answers now!

( x 3 21 x 2 + 147 x 343 ) ÷ ( x 7 )

x 2 14 x + 49

Got questions? Get instant answers now!

( x 3 15 x 2 + 75 x 125 ) ÷ ( x 5 )

Got questions? Get instant answers now!

( 9 x 3 x + 2 ) ÷ ( 3 x 1 )

3 x 2 + x + 2 3 x 1

Got questions? Get instant answers now!

( 6 x 3 x 2 + 5 x + 2 ) ÷ ( 3 x + 1 )

Got questions? Get instant answers now!

( x 4 + x 3 3 x 2 2 x + 1 ) ÷ ( x + 1 )

x 3 3 x + 1

Got questions? Get instant answers now!

( x 4 3 x 2 + 1 ) ÷ ( x 1 )

Got questions? Get instant answers now!

( x 4 + 2 x 3 3 x 2 + 2 x + 6 ) ÷ ( x + 3 )

x 3 x 2 + 2

Got questions? Get instant answers now!

( x 4 10 x 3 + 37 x 2 60 x + 36 ) ÷ ( x 2 )

Got questions? Get instant answers now!

( x 4 8 x 3 + 24 x 2 32 x + 16 ) ÷ ( x 2 )

x 3 6 x 2 + 12 x 8

Got questions? Get instant answers now!

( x 4 + 5 x 3 3 x 2 13 x + 10 ) ÷ ( x + 5 )

Got questions? Get instant answers now!

( x 4 12 x 3 + 54 x 2 108 x + 81 ) ÷ ( x 3 )

x 3 9 x 2 + 27 x 27

Got questions? Get instant answers now!

( 4 x 4 2 x 3 4 x + 2 ) ÷ ( 2 x 1 )

Got questions? Get instant answers now!

( 4 x 4 + 2 x 3 4 x 2 + 2 x + 2 ) ÷ ( 2 x + 1 )

2 x 3 2 x + 2

Got questions? Get instant answers now!

For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization.

x 2 , 4 x 3 3 x 2 8 x + 4

Got questions? Get instant answers now!

x 2 , 3 x 4 6 x 3 5 x + 10

Yes ( x 2 ) ( 3 x 3 5 )

Got questions? Get instant answers now!

x + 3 , 4 x 3 + 5 x 2 + 8

Got questions? Get instant answers now!

x 2 , 4 x 4 15 x 2 4

Yes ( x 2 ) ( 4 x 3 + 8 x 2 + x + 2 )

Got questions? Get instant answers now!

x 1 2 , 2 x 4 x 3 + 2 x 1

Got questions? Get instant answers now!

x + 1 3 , 3 x 4 + x 3 3 x + 1

No

Got questions? Get instant answers now!

Graphical

For the following exercises, use the graph of the third-degree polynomial and one factor to write the factored form of the polynomial suggested by the graph. The leading coefficient is one.

Factor is x 2 x + 3

Graph of a polynomial that has a x-intercept at -1.
Got questions? Get instant answers now!

Factor is ( x 2 + 2 x + 4 )

Graph of a polynomial that has a x-intercept at 1.

( x 1 ) ( x 2 + 2 x + 4 )

Got questions? Get instant answers now!

Factor is x 2 + 2 x + 5

Graph of a polynomial that has a x-intercept at 2.
Got questions? Get instant answers now!

Factor is x 2 + x + 1

Graph of a polynomial that has a x-intercept at 5.

( x 5 ) ( x 2 + x + 1 )

Got questions? Get instant answers now!

For the following exercises, use synthetic division to find the quotient and remainder.

4 x 3 33 x 2

Quotient: 4 x 2 + 8 x + 16 , remainder: 1

Got questions? Get instant answers now!

3 x 3 + 2 x 5 x 1

Quotient: 3 x 2 + 3 x + 5 , remainder: 0

Got questions? Get instant answers now!

4 x 3 x 2 12 x + 4

Got questions? Get instant answers now!

x 4 22 x + 2

Quotient: x 3 2 x 2 + 4 x 8 , remainder: 6

Got questions? Get instant answers now!

Technology

For the following exercises, use a calculator with CAS to answer the questions.

Consider x k 1 x 1 with k = 1 ,   2 ,   3. What do you expect the result to be if k = 4 ?

Got questions? Get instant answers now!

Consider x k + 1 x + 1 for k = 1 ,   3 ,   5. What do you expect the result to be if k = 7 ?

x 6 x 5 + x 4 x 3 + x 2 x + 1

Got questions? Get instant answers now!

Consider x 4 k 4 x k for k = 1 ,   2 ,   3. What do you expect the result to be if k = 4 ?

Got questions? Get instant answers now!

Consider x k x + 1 with k = 1 ,   2 ,   3. What do you expect the result to be if k = 4 ?

x 3 x 2 + x 1 + 1 x + 1

Got questions? Get instant answers now!

Consider x k x 1 with k = 1 ,   2 ,   3. What do you expect the result to be if k = 4 ?

Got questions? Get instant answers now!

Extensions

For the following exercises, use synthetic division to determine the quotient involving a complex number.

x + 1 x i

1 + 1 + i x i

Got questions? Get instant answers now!

x + 1 x + i

1 + 1 i x + i

Got questions? Get instant answers now!

x 3 + 1 x i

x 2 i x 1 + 1 i x i

Got questions? Get instant answers now!

Real-world applications

For the following exercises, use the given length and area of a rectangle to express the width algebraically.

Length is x + 5 , area is 2 x 2 + 9 x 5.

Got questions? Get instant answers now!

Length is 2 x   +   5 , area is 4 x 3 + 10 x 2 + 6 x + 15

2 x 2 + 3

Got questions? Get instant answers now!

Length is 3 x 4 , area is 6 x 4 8 x 3 + 9 x 2 9 x 4

Got questions? Get instant answers now!

For the following exercises, use the given volume of a box and its length and width to express the height of the box algebraically.

Volume is 12 x 3 + 20 x 2 21 x 36 , length is 2 x + 3 , width is 3 x 4.

2 x + 3

Got questions? Get instant answers now!

Volume is 18 x 3 21 x 2 40 x + 48 , length is 3 x 4 , width is 3 x 4.

Got questions? Get instant answers now!

Volume is 10 x 3 + 27 x 2 + 2 x 24 , length is 5 x 4 , width is 2 x + 3.

x + 2

Got questions? Get instant answers now!

Volume is 10 x 3 + 30 x 2 8 x 24 , length is 2 , width is x + 3.

Got questions? Get instant answers now!

For the following exercises, use the given volume and radius of a cylinder to express the height of the cylinder algebraically.

Volume is π ( 25 x 3 65 x 2 29 x 3 ) , radius is 5 x + 1.

x 3

Got questions? Get instant answers now!

Volume is π ( 4 x 3 + 12 x 2 15 x 50 ) , radius is 2 x + 5.

Got questions? Get instant answers now!

Volume is π ( 3 x 4 + 24 x 3 + 46 x 2 16 x 32 ) , radius is x + 4.

3 x 2 2

Got questions? Get instant answers now!

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
explain assimilatory nitrate reduction
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
what is cell
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
Musa
what are emergency diseases
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 ❣️
_Adnan
define infection ,prevention and control
Innocent
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
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 2

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask