<< Chapter < Page Chapter >> Page >

Evaluate 3 x 2 9 x + 7 when

  1. x = 3
  2. x = −1

Solution

x = 3
3 x 2 9 x + 7
Substitute 3 for x 3 ( 3 ) 2 9 ( 3 ) + 7
Simplify the expression with the exponent. 3 · 9 9 ( 3 ) + 7
Multiply. 27 27 + 7
Simplify. 7
x = −1
3 x 2 9 x + 7
Substitute −1 for x 3 ( −1 ) 2 9 ( −1 ) + 7
Simplify the expression with the exponent. 3 · 1 9 ( −1 ) + 7
Multiply. 3 + 9 + 7
Simplify. 19
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Evaluate: 2 x 2 + 4 x 3 when

  1. x = 2
  2. x = −3

  1. 13
  2. 3

Got questions? Get instant answers now!

Evaluate: 7 y 2 y 2 when

  1. y = −4
  2. y = 0

  1. 114
  2. −2

Got questions? Get instant answers now!

The polynomial −16 t 2 + 300 gives the height of an object t seconds after it is dropped from a 300 foot tall bridge. Find the height after t = 3 seconds.

Solution

.
Substitute 3 for t .
Simplify the expression with the exponent. .
Multiply. .
Simplify. .
Got questions? Get instant answers now!
Got questions? Get instant answers now!

The polynomial −8 t 2 + 24 t + 4 gives the height, in feet, of a ball t seconds after it is tossed into the air, from an initial height of 4 feet. Find the height after t = 3 seconds.

4 feet

Got questions? Get instant answers now!

The polynomial −8 t 2 + 24 t + 4 gives the height, in feet, of a ball x seconds after it is tossed into the air, from an initial height of 4 feet. Find the height after t = 2 seconds.

20 feet

Got questions? Get instant answers now!

Access additional online resources

Practice makes perfect

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the polynomials is a monomial, binomial, trinomial, or other polynomial.

a 2 + 9 a + 18

trinomial

Got questions? Get instant answers now!

y 3 8 y 2 + 2 y 16

polynomial

Got questions? Get instant answers now!

m 4 + 4 m 3 + 6 m 2 + 4 m + 1

Got questions? Get instant answers now!

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

5 c 3 + 11 c 2 c 8

Got questions? Get instant answers now!

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Add: 4 a , 3 b , 8 a

−4 a −3 b

Got questions? Get instant answers now!

Add: 4 x , 3 y , 3 x

Got questions? Get instant answers now!

Subtract 5 x 6 from 12 x 6

−17 x 6

Got questions? Get instant answers now!

Subtract 2 p 4 from 7 p 4

Got questions? Get instant answers now!

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

( 4 y 2 + 10 y + 3 ) + ( 8 y 2 6 y + 5 )

12 y 2 + 4 y + 8

Got questions? Get instant answers now!

( 7 x 2 9 x + 2 ) + ( 6 x 2 4 x + 3 )

Got questions? Get instant answers now!

( x 2 + 6 x + 8 ) + ( −4 x 2 + 11 x 9 )

−3 x 2 + 17 x − 1

Got questions? Get instant answers now!

( y 2 + 9 y + 4 ) + ( −2 y 2 5 y 1 )

Got questions? Get instant answers now!

( 3 a 2 + 7 ) + ( a 2 7 a 18 )

4 a 2 − 7 a − 11

Got questions? Get instant answers now!

( p 2 5 p 11 ) + ( 3 p 2 + 9 )

Got questions? Get instant answers now!

( 6 m 2 9 m 3 ) ( 2 m 2 + m 5 )

4 m 2 − 10 m + 2

Got questions? Get instant answers now!

( 3 n 2 4 n + 1 ) ( 4 n 2 n 2 )

Got questions? Get instant answers now!

( z 2 + 8 z + 9 ) ( z 2 3 z + 1 )

11 z + 8

Got questions? Get instant answers now!

( z 2 7 z + 5 ) ( z 2 8 z + 6 )

Got questions? Get instant answers now!

( 12 s 2 15 s ) ( s 9 )

12 s 2 − 16 s + 9

Got questions? Get instant answers now!

( 10 r 2 20 r ) ( r 8 )

Got questions? Get instant answers now!

Find the sum of ( 2 p 3 8 ) and ( p 2 + 9 p + 18 )

2 p 3 + p 2 + 9 p + 10

Got questions? Get instant answers now!

Find the sum of ( q 2 + 4 q + 13 ) and ( 7 q 3 3 )

Got questions? Get instant answers now!

Subtract ( 7 x 2 4 x + 2 ) from ( 8 x 2 x + 6 )

x 2 + 3 x + 4

Got questions? Get instant answers now!

Subtract ( 5 x 2 x + 12 ) from ( 9 x 2 6 x 20 )

Got questions? Get instant answers now!

Find the difference of ( w 2 + w 42 ) and ( w 2 10 w + 24 )

11 w − 66

Got questions? Get instant answers now!

Find the difference of ( z 2 3 z 18 ) and ( z 2 + 5 z 20 )

Got questions? Get instant answers now!

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Evaluate 8 y 2 3 y + 2

  1. y = 5
  2. y = −2
  3. y = 0

  1. 187
  2. 40
  3. 2

Got questions? Get instant answers now!

Evaluate 5 y 2 y 7 when:

  1. y = −4
  2. y = 1
  3. y = 0

Got questions? Get instant answers now!

Evaluate 4 36 x when:

  1. x = 3
  2. x = 0
  3. x = −1

  1. −104
  2. 4
  3. 40

Got questions? Get instant answers now!

Evaluate 16 36 x 2 when:

  1. x = −1
  2. x = 0
  3. x = 2

Got questions? Get instant answers now!

A window washer drops a squeegee from a platform 275 feet high. The polynomial −16 t 2 + 275 gives the height of the squeegee t seconds after it was dropped. Find the height after t = 4 seconds.

19 feet

Got questions? Get instant answers now!

A manufacturer of microwave ovens has found that the revenue received from selling microwaves at a cost of p dollars each is given by the polynomial −5 p 2 + 350 p . Find the revenue received when p = 50 dollars.

Got questions? Get instant answers now!

Everyday math

Fuel Efficiency The fuel efficiency (in miles per gallon) of a bus going at a speed of x miles per hour is given by the polynomial 1 160 x 2 + 1 2 x . Find the fuel efficiency when x = 40 mph.

10 mpg

Got questions? Get instant answers now!

Stopping Distance The number of feet it takes for a car traveling at x miles per hour to stop on dry, level concrete is given by the polynomial 0.06 x 2 + 1.1 x . Find the stopping distance when x = 60 mph.

Got questions? Get instant answers now!

Writing exercises

Using your own words, explain the difference between a monomial, a binomial, and a trinomial.

Answers will vary.

Got questions? Get instant answers now!

Eloise thinks the sum 5 x 2 + 3 x 4 is 8 x 6 . What is wrong with her reasoning?

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Questions & Answers

Leo Robinson's definition
Adejimi Reply
how is equilibrium defined in financial markets?
Babakura Reply
the concept of it
DALOM
Country A has export sales 20 billion, government purchases 1000billion, business investment is 50 billion, imports are 40billion, and consumption spending is 2000billin. What is the dollar value of GDP ?
Habtamu Reply
what is determination of national income?
Waqar Reply
economic growth
Rukaiya
stock of capital
Rukaiya
we're RBI keep money with them
Anil
Y =C+l
Favour
evaluate the success affirmative action as one of south Africa's redress method
Tebatso Reply
what is market equilibrium
explorer Reply
it is a situation in which the supply of an item is exactly equal to it dd .
Ssmith
inder wat condition shld a firm stop production in both short n lungrun ?
Ssmith
what is 2nd degree price discrimination?
Ssmith
what is quantity
Tettey
what is quantity2
Deji Reply
An indefinite amount of something.
explorer
what is demand
Kaman Reply
in ordinary sense demand means desire
Khalid
demand in economics means both willingness as well as the ability to purchase a commodity by paying a price an also its actuall purchase
Khalid
what is absolute advantage
Khalid
demand refers to the various quantity of goods and services that consumers are willing and able to purchase at a particular period of time all other things been equal
Dela
The amount of a good or service that consumers are willing to buy at a particular price.
explorer
what is cost pull inflation?
oru
what is utility
oru
what is cost pull inflation?
oru
demand is economic principle referring to a consumer's desire and willingness to pay a price for a specific or service..
Babakura
utility is the among of certisfaction driving from using a comundity
Anas
pull cost of inflation hight population unemployment to some of The country members poor government system
Anas
what is a buffer scheme
Lukong
state the second law of demand and supply
Ahmadou Reply
state the law of diminishing marginal utility
Ahmadou
dt know WATS the answer
Rukundo
mention and explain two Bank I financial institutions and two non baking financial institutions
Onah Reply
wat is demand pull inflation
Tony Reply
Demand-pull inflation is asserted to arise when aggregate demandin an economy outpaces aggregate supply. It involvesinflation rising as real gross domestic product rises and unemployment falls, as the economy moves along the Phillips curve.
kevin
Perfectly elastic demand
Abubakar Reply
this is a form of demand where goods are demanded at a constant price
Rukundo
what inelastic demanding
Koire
demand of any good demanded more after a certain period. if a commodity prices may high and scarcity of that resources.
Anil
cannot demand more
Anil
what is cross-elasticity of demand
Miles Reply
cross elasticity of demand is an economic concept that measures the responsiveness in the quantity demand of one good when a change in price takes place in other good
Mallekha
this is responsiveness quantity demanded keeping other factors constant
Rukundo
what economic growth
Rukundo Reply
conditions of perfect market
NdzAlama Reply
CONDITIONS OF PERFECT MARKET: 1. Perfect competition(PC): no increasing returns, many buyers and sellers, all are price takers, not prices makers. 2. Perfect Information (PI): buyers and sellers know all they need to know about what they are buying and selling to make the right decisions.
Mallekha
3. Complete Markets(CM): no externalities or public goods, no transactions costs, "thick" markets.
Mallekha
nice contributor
Mohammed
A numerous downsized market that does not meet standards.
LaTasha
A Perfect Market is a numerous downsized market that does not meet standards.
LaTasha
what is a market
Ahmadou
is place where buyers and sellers met together for the purpose of buying and selling of good and services
Babakura
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
Practice Key Terms 7

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask