<< Chapter < Page Chapter >> Page >

( x 4 1 ) ÷ ( x 4 )

255

Got questions? Get instant answers now!

( 3 x 3 + 4 x 2 8 x + 2 ) ÷ ( x 3 )

Got questions? Get instant answers now!

( 4 x 3 + 5 x 2 2 x + 7 ) ÷ ( x + 2 )

1

Got questions? Get instant answers now!

For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.

f ( x ) = 2 x 3 9 x 2 + 13 x 6 ;   x 1

Got questions? Get instant answers now!

f ( x ) = 2 x 3 + x 2 5 x + 2 ;   x + 2

2 ,   1 ,   1 2

Got questions? Get instant answers now!

f ( x ) = 3 x 3 + x 2 20 x + 12 ;   x + 3

Got questions? Get instant answers now!

f ( x ) = 2 x 3 + 3 x 2 + x + 6 ; x + 2

2

Got questions? Get instant answers now!

f ( x ) = 5 x 3 + 16 x 2 9 ; x 3

Got questions? Get instant answers now!

x 3 + 3 x 2 + 4 x + 12 ; x + 3

3

Got questions? Get instant answers now!

4 x 3 7 x + 3 ; x 1

Got questions? Get instant answers now!

2 x 3 + 5 x 2 12 x 30 , 2 x + 5

5 2 ,   6 ,   6

Got questions? Get instant answers now!

For the following exercises, use the Rational Zero Theorem to find all real zeros.

x 3 3 x 2 10 x + 24 = 0

Got questions? Get instant answers now!

2 x 3 + 7 x 2 10 x 24 = 0

2 ,   4 ,   3 2

Got questions? Get instant answers now!

x 3 + 2 x 2 9 x 18 = 0

Got questions? Get instant answers now!

x 3 + 5 x 2 16 x 80 = 0

4 ,   4 ,   5

Got questions? Get instant answers now!

x 3 3 x 2 25 x + 75 = 0

Got questions? Get instant answers now!

2 x 3 3 x 2 32 x 15 = 0

5 ,   3 ,   1 2

Got questions? Get instant answers now!

2 x 3 + x 2 7 x 6 = 0

Got questions? Get instant answers now!

2 x 3 3 x 2 x + 1 = 0

1 2 ,   1 + 5 2 ,   1 5 2

Got questions? Get instant answers now!

3 x 3 x 2 11 x 6 = 0

Got questions? Get instant answers now!

2 x 3 5 x 2 + 9 x 9 = 0

3 2

Got questions? Get instant answers now!

2 x 3 3 x 2 + 4 x + 3 = 0

Got questions? Get instant answers now!

x 4 2 x 3 7 x 2 + 8 x + 12 = 0

2 ,   3 ,   1 ,   2

Got questions? Get instant answers now!

x 4 + 2 x 3 9 x 2 2 x + 8 = 0

Got questions? Get instant answers now!

4 x 4 + 4 x 3 25 x 2 x + 6 = 0

1 2 ,   1 2 ,   2 ,   3

Got questions? Get instant answers now!

2 x 4 3 x 3 15 x 2 + 32 x 12 = 0

Got questions? Get instant answers now!

x 4 + 2 x 3 4 x 2 10 x 5 = 0

1 ,   1 ,   5 ,   5

Got questions? Get instant answers now!

8 x 4 + 26 x 3 + 39 x 2 + 26 x + 6

3 4 ,   1 2

Got questions? Get instant answers now!

For the following exercises, find all complex solutions (real and non-real).

x 3 8 x 2 + 25 x 26 = 0

2 ,   3 + 2 i ,   3 2 i

Got questions? Get instant answers now!

x 3 + 13 x 2 + 57 x + 85 = 0

Got questions? Get instant answers now!

3 x 3 4 x 2 + 11 x + 10 = 0

2 3 ,   1 + 2 i ,   1 2 i

Got questions? Get instant answers now!

x 4 + 2 x 3 + 22 x 2 + 50 x 75 = 0

Got questions? Get instant answers now!

2 x 3 3 x 2 + 32 x + 17 = 0

1 2 ,   1 + 4 i ,   1 4 i

Got questions? Get instant answers now!

Graphical

For the following exercises, use Descartes’ Rule to determine the possible number of positive and negative solutions. Confirm with the given graph.

f ( x ) = x 4 x 2 1

1 positive, 1 negative

Graph of f(x)=x^4-x^2-1.
Got questions? Get instant answers now!

f ( x ) = x 3 2 x 2 5 x + 6

Got questions? Get instant answers now!

f ( x ) = x 3 2 x 2 + x 1

3 or 1 positive, 0 negative

Graph of f(x)=x^3-2x^2+x-1.
Got questions? Get instant answers now!

f ( x ) = x 4 + 2 x 3 12 x 2 + 14 x 5

Got questions? Get instant answers now!

f ( x ) = 2 x 3 + 37 x 2 + 200 x + 300

0 positive, 3 or 1 negative

Graph of f(x)=2x^3+37x^2+200x+300.
Got questions? Get instant answers now!

f ( x ) = x 3 2 x 2 16 x + 32

Got questions? Get instant answers now!

f ( x ) = 2 x 4 5 x 3 5 x 2 + 5 x + 3

2 or 0 positive, 2 or 0 negative

Graph of f(x)=2x^4-5x^3-5x^2+5x+3.
Got questions? Get instant answers now!

f ( x ) = 2 x 4 5 x 3 14 x 2 + 20 x + 8

Got questions? Get instant answers now!

f ( x ) = 10 x 4 21 x 2 + 11

2 or 0 positive, 2 or 0 negative

Graph of f(x)=10x^4-21x^2+11.
Got questions? Get instant answers now!

Numeric

For the following exercises, list all possible rational zeros for the functions.

f ( x ) = x 4 + 3 x 3 4 x + 4

Got questions? Get instant answers now!

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

± 5 ,   ± 1 ,   ± 5 2

Got questions? Get instant answers now!

f ( x ) = 3 x 3 + 5 x 2 5 x + 4

Got questions? Get instant answers now!

f ( x ) = 6 x 4 10 x 2 + 13 x + 1

± 1 ,   ± 1 2 ,   ± 1 3 ,   ± 1 6

Got questions? Get instant answers now!

f ( x ) = 4 x 5 10 x 4 + 8 x 3 + x 2 8

Got questions? Get instant answers now!

Technology

For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rational zeros. All real solutions are rational.

f ( x ) = 6 x 3 7 x 2 + 1

1 ,   1 2 ,   1 3

Got questions? Get instant answers now!

f ( x ) = 4 x 3 4 x 2 13 x 5

Got questions? Get instant answers now!

f ( x ) = 8 x 3 6 x 2 23 x + 6

2 ,   1 4 ,   3 2

Got questions? Get instant answers now!

f ( x ) = 12 x 4 + 55 x 3 + 12 x 2 117 x + 54

Got questions? Get instant answers now!

f ( x ) = 16 x 4 24 x 3 + x 2 15 x + 25

5 4

Got questions? Get instant answers now!

Extensions

For the following exercises, construct a polynomial function of least degree possible using the given information.

Real roots: –1, 1, 3 and ( 2 , f ( 2 ) ) = ( 2 , 4 )

Got questions? Get instant answers now!

Real roots: –1 (with multiplicity 2 and 1) and ( 2 , f ( 2 ) ) = ( 2 , 4 )

f ( x ) = 4 9 ( x 3 + x 2 x 1 )

Got questions? Get instant answers now!

Real roots: –2, 1 2 (with multiplicity 2) and ( 3 , f ( 3 ) ) = ( 3 , 5 )

Got questions? Get instant answers now!

Real roots: 1 2 , 0, 1 2 and ( 2 , f ( 2 ) ) = ( 2 , 6 )

f ( x ) = 1 5 ( 4 x 3 x )

Got questions? Get instant answers now!

Real roots: –4, –1, 1, 4 and ( 2 , f ( 2 ) ) = ( 2 , 10 )

Got questions? Get instant answers now!

Real-world applications

For the following exercises, find the dimensions of the box described.

The length is twice as long as the width. The height is 2 inches greater than the width. The volume is 192 cubic inches.

8 by 4 by 6 inches

Got questions? Get instant answers now!

The length, width, and height are consecutive whole numbers. The volume is 120 cubic inches.

Got questions? Get instant answers now!

The length is one inch more than the width, which is one inch more than the height. The volume is 86.625 cubic inches.

5.5 by 4.5 by 3.5 inches

Got questions? Get instant answers now!

The length is three times the height and the height is one inch less than the width. The volume is 108 cubic inches.

Got questions? Get instant answers now!

The length is 3 inches more than the width. The width is 2 inches more than the height. The volume is 120 cubic inches.

8 by 5 by 3 inches

Got questions? Get instant answers now!

For the following exercises, find the dimensions of the right circular cylinder described.

The radius is 3 inches more than the height. The volume is 16 π cubic meters.

Got questions? Get instant answers now!

The height is one less than one half the radius. The volume is 72 π cubic meters.

Radius = 6 meters, Height = 2 meters

Got questions? Get instant answers now!

The radius and height differ by one meter. The radius is larger and the volume is 48 π cubic meters.

Got questions? Get instant answers now!

The radius and height differ by two meters. The height is greater and the volume is 28.125 π cubic meters.

Radius = 2.5 meters, Height = 4.5 meters

Got questions? Get instant answers now!

The radius is 1 3 meter greater than the height. The volume is 98 9 π cubic meters.

Got questions? Get instant answers now!

Questions & Answers

sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
Thanks for this helpfull app
Axmed Reply
secA+tanA=2√5,sinA=?
richa Reply
tan2a+tan2a=√3
Rahulkumar
classes of function
Yazidu
if sinx°=sin@, then @ is - ?
NAVJIT Reply
the value of tan15°•tan20°•tan70°•tan75° -
NAVJIT
0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
Practice Key Terms 6

Get the best Algebra and trigonometry course in your pocket!





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