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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
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Evaluate: 2 x 2 + 4 x 3 when

  1. x = 2
  2. x = −3

  1. 13
  2. 3

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Evaluate: 7 y 2 y 2 when

  1. y = −4
  2. y = 0

  1. 114
  2. −2

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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. .
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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

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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

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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

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y 3 8 y 2 + 2 y 16

polynomial

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

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Determine the Degree of Polynomials

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

5 c 3 + 11 c 2 c 8

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Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

Add: 4 a , 3 b , 8 a

−4 a −3 b

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Add: 4 x , 3 y , 3 x

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Subtract 5 x 6 from 12 x 6

−17 x 6

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Subtract 2 p 4 from 7 p 4

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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

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

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

−3 x 2 + 17 x − 1

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( y 2 + 9 y + 4 ) + ( −2 y 2 5 y 1 )

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

4 a 2 − 7 a − 11

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

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

4 m 2 − 10 m + 2

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

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

11 z + 8

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

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( 12 s 2 15 s ) ( s 9 )

12 s 2 − 16 s + 9

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( 10 r 2 20 r ) ( r 8 )

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

2 p 3 + p 2 + 9 p + 10

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

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

x 2 + 3 x + 4

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

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

11 w − 66

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

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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

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Evaluate 5 y 2 y 7 when:

  1. y = −4
  2. y = 1
  3. y = 0

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Evaluate 4 36 x when:

  1. x = 3
  2. x = 0
  3. x = −1

  1. −104
  2. 4
  3. 40

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Evaluate 16 36 x 2 when:

  1. x = −1
  2. x = 0
  3. x = 2

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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

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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.

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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

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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.

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Writing exercises

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

Answers will vary.

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

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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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How do i figure this problem out.
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why surface tension is zero at critical temperature
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Practice Key Terms 7

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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