<< Chapter < Page Chapter >> Page >

Practice makes perfect

Identify Polynomials, Monomials, Binomials, and Trinomials

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


81 b 5 24 b 3 + 1
5 c 3 + 11 c 2 c 8
14 15 y + 1 7
5
4 y + 17

trinomial polynomial binomial monomial binomial

Got questions? Get instant answers now!


x 2 y 2
−13 c 4
x 2 + 5 x 7
x 2 y 2 2 x y + 8
19

Got questions? Get instant answers now!


8 3 x
z 2 5 z 6
y 3 8 y 2 + 2 y 16
81 b 5 24 b 3 + 1
−18

binomial trinomial polynomial trinomial monomial

Got questions? Get instant answers now!


11 y 2
−73
6 x 2 3 x y + 4 x 2 y + y 2
4 y + 17
5 c 3 + 11 c 2 c 8

Got questions? Get instant answers now!

Determine the Degree of Polynomials

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


6 a 2 + 12 a + 14
18 x y 2 z
5 x + 2
y 3 8 y 2 + 2 y 16
−24

2 4 1 3 0

Got questions? Get instant answers now!


9 y 3 10 y 2 + 2 y 6
−12 p 4
a 2 + 9 a + 18
20 x 2 y 2 10 a 2 b 2 + 30
17

Got questions? Get instant answers now!


14 29 x
z 2 5 z 6
y 3 8 y 2 + 2 y 16
23 a b 2 14
−3

1 2 3 3 0

Got questions? Get instant answers now!


62 y 2
15
6 x 2 3 x y + 4 x 2 y + y 2
10 9 x
m 4 + 4 m 3 + 6 m 2 + 4 m + 1

Got questions? Get instant answers now!

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

28 x ( −12 x )

40 x

Got questions? Get instant answers now!

12 a + 5 b 22 a

−10a + 5 b

Got questions? Get instant answers now!

2 a 2 + b 2 6 a 2

−4 a 2 + b 2

Got questions? Get instant answers now!

x y 2 5 x 5 y 2

x y 2 5 x 5 y 2

Got questions? Get instant answers now!

a 2 b 4 a 5 a b 2

a 2 b 4 a 5 a b 2

Got questions? Get instant answers now!

Add: 4 a , −3 b , −8 a

−4 a 3 b

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.

( 5 y 2 + 12 y + 4 ) + ( 6 y 2 8 y + 7 )

11 y 2 + 4 y + 11

Got questions? Get instant answers now!

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

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!

( 8 x 2 5 x + 2 ) + ( 3 x 2 + 3 )

11 x 2 5 x + 5

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( 5 a 2 + 8 ) + ( a 2 4 a 9 )

6 a 2 4 a 1

Got questions? Get instant answers now!

( p 2 6 p 18 ) + ( 2 p 2 + 11 )

Got questions? Get instant answers now!

( 4 m 2 6 m 3 ) ( 2 m 2 + m 7 )

2 m 2 7 m + 4

Got questions? Get instant answers now!

( 3 b 2 4 b + 1 ) ( 5 b 2 b 2 )

Got questions? Get instant answers now!

( a 2 + 8 a + 5 ) ( a 2 3 a + 2 )

5 a + 3

Got questions? Get instant answers now!

( b 2 7 b + 5 ) ( b 2 2 b + 9 )

Got questions? Get instant answers now!

( 12 s 2 15 s ) ( s 9 )

12 s 2 14 s + 9

Got questions? Get instant answers now!

( 10 r 2 20 r ) ( r 8 )

Got questions? Get instant answers now!

Subtract ( 9 x 2 + 2 ) from ( 12 x 2 x + 6 ) .

3 x 2 x + 4

Got questions? Get instant answers now!

Subtract ( 5 y 2 y + 12 ) from ( 10 y 2 8 y 20 ) .

Got questions? Get instant answers now!

Subtract ( 7 w 2 4 w + 2 ) from ( 8 w 2 w + 6 ) .

w 2 + 3 w + 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 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!

Find the sum of ( 8 a 3 8 a ) and ( a 2 + 6 a + 12 ) .

8 a 3 + a 2 2 a + 12

Got questions? Get instant answers now!

Find the sum of
( b 2 + 5 b + 13 ) and ( 4 b 3 6 ) .

Got questions? Get instant answers now!

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

11 w 64

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!

Find the difference of
( c 2 + 4 c 33 ) and
( c 2 8 c + 12 ) .

12 c 45

Got questions? Get instant answers now!

Find the difference of
( t 2 5 t 15 ) and
( t 2 + 4 t 17 ) .

Got questions? Get instant answers now!

( 7 x 2 2 x y + 6 y 2 ) + ( 3 x 2 5 x y )

10 x 2 7 x y + 6 y 2

Got questions? Get instant answers now!

( −5 x 2 4 x y 3 y 2 ) + ( 2 x 2 7 x y )

Got questions? Get instant answers now!

( 7 m 2 + m n 8 n 2 ) + ( 3 m 2 + 2 m n )

10 m 2 + 3 m n 8 n 2

Got questions? Get instant answers now!

( 2 r 2 3 r s 2 s 2 ) + ( 5 r 2 3 r s )

Got questions? Get instant answers now!

( a 2 b 2 ) ( a 2 + 3 a b 4 b 2 )

−3 a b + 3 b 2

Got questions? Get instant answers now!

( m 2 + 2 n 2 ) ( m 2 8 m n n 2 )

Got questions? Get instant answers now!

( u 2 v 2 ) ( u 2 4 u v 3 v 2 )

4 u v + 2 v 2

Got questions? Get instant answers now!

( j 2 k 2 ) ( j 2 8 j k 5 k 2 )

Got questions? Get instant answers now!

( p 3 3 p 2 q ) + ( 2 p q 2 + 4 q 3 ) ( 3 p 2 q + p q 2 )

p 3 6 p 2 q + p q 2 + 4 q 3

Got questions? Get instant answers now!

( a 3 2 a 2 b ) + ( a b 2 + b 3 ) ( 3 a 2 b + 4 a b 2 )

Got questions? Get instant answers now!

( x 3 x 2 y ) ( 4 x y 2 y 3 ) + ( 3 x 2 y x y 2 )

x 3 + 2 x 2 y 5 x y 2 + y 3

Got questions? Get instant answers now!

( x 3 2 x 2 y ) ( x y 2 3 y 3 ) ( x 2 y 4 x y 2 )

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 when:

y = 5
y = −2
y = 0

187 46 2

Got questions? Get instant answers now!

Evaluate 5 y 2 y 7 when:

y = −4
y = 1
y = 0

Got questions? Get instant answers now!

Evaluate 4 36 x when:

x = 3
x = 0
x = −1

−104 4 40

Got questions? Get instant answers now!

Evaluate 16 36 x 2 when:

x = −1
x = 0
x = 2

Got questions? Get instant answers now!

A painter drops a brush from a platform 75 feet high. The polynomial −16 t 2 + 75 gives the height of the brush t seconds after it was dropped. Find the height after t = 2 seconds.

11

Got questions? Get instant answers now!

A girl drops a ball off a cliff into the ocean. The polynomial −16 t 2 + 250 gives the height of a ball t seconds after it is dropped from a 250-foot tall cliff. Find the height after t = 2 seconds.

Got questions? Get instant answers now!

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial −4 p 2 + 420 p . Find the revenue received when p = 60 dollars.

$10,800

Got questions? Get instant answers now!

A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial −4 p 2 + 420 p . Find the revenue received when p = 90 dollars.

Got questions? Get instant answers now!

Everyday math

Fuel Efficiency The fuel efficiency (in miles per gallon) of a car going at a speed of x miles per hour is given by the polynomial 1 150 x 2 + 1 3 x . Find the fuel efficiency when x = 30 mph .

4

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 = 40 mph .

Got questions? Get instant answers now!

Rental Cost The cost to rent a rug cleaner for d days is given by the polynomial 5.50 d + 25 . Find the cost to rent the cleaner for 6 days.

$58

Got questions? Get instant answers now!

Height of Projectile The height (in feet) of an object projected upward is given by the polynomial −16 t 2 + 60 t + 90 where t represents time in seconds. Find the height after t = 2.5 seconds.

Got questions? Get instant answers now!

Temperature Conversion The temperature in degrees Fahrenheit is given by the polynomial 9 5 c + 32 where c represents the temperature in degrees Celsius. Find the temperature in degrees Fahrenheit when c = 65 ° .

149

Got questions? Get instant answers now!

Writing exercises

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

Got questions? Get instant answers now!

Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.

Answers will vary.

Got questions? Get instant answers now!

Ariana thinks the sum 6 y 2 + 5 y 4 is 11 y 6 . What is wrong with her reasoning?

Got questions? Get instant answers now!

Jonathan thinks that 1 3 and 1 x are both monomials. What is wrong with his reasoning?

Answers will vary.

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.

This is a table that has six rows and four columns. In the first row, which is a header row, the cells read from left to right “I can…,” “Confidently,” “With some help,” and “No-I don’t get it!” The first column below “I can…” reads “identify polynomials, monomials, binomials, and trinomials,” “determine the degree of polynomials,” “add and subtract monomials,” “add and subtract polynomials,” and “evaluate a polynomial for a given value.” The rest of the cells are blank.

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

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
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
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Can you all help me I don't get any of this
Jade Reply
4^×=9
Alberto Reply
Did anyone else have trouble getting in quiz link for linear inequalities?
Sireka Reply
operation of trinomial
Justin Reply
y=2×+9
Jacob Reply
Keshad gets paid $2,400 per month plus 6% of his sales. His brother earns $3,300 per month. For what amount of total sales will Keshad’s monthly pay be higher than his brother’s monthly pay?
Hector Reply
Mayra has $124 in her checking account. She writes a check for $152. What is the New Balance in her checking account?
REVOLUTION Reply
Practice Key Terms 8

Get the best Elementary algebra course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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