<< 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

Why is b in the answer
Dahsolar Reply
how do you work it out?
Brad Reply
answer
Ernest
heheheehe
Nitin
(Pcos∅+qsin∅)/(pcos∅-psin∅)
John Reply
how to do that?
Rosemary Reply
what is it about?
Amoah
how to answer the activity
Chabelita Reply
how to solve the activity
Chabelita
solve for X,,4^X-6(2^)-16=0
Alieu Reply
x4xminus 2
Lominate
sobhan Singh jina uniwarcity tignomatry ka long answers tile questions
harish Reply
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
ZAHRO Reply
If  , , are the roots of the equation 3 2 0, x px qx r     Find the value of 1  .
Swetha Reply
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Patrick Reply
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
how I can simplify algebraic expressions
Katleho Reply
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
Mary Reply
23yrs
Yeboah
lairenea's age is 23yrs
ACKA
hy
Katleho
Ello everyone
Katleho
Laurene is 46 yrs and Mae is 23 is
Solomon
hey people
christopher
age does not matter
christopher
solve for X, 4^x-6(2*)-16=0
Alieu
prove`x^3-3x-2cosA=0 (-π<A<=π
Mayank Reply
create a lesson plan about this lesson
Rose Reply
Excusme but what are you wrot?
Practice Key Terms 6

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