Determine whether each expression is a
polynomial. If it is a polynomial, find the degree
and determine whether it is a monomial,
binomial, or trinomial.
1.7ab + 6b2 – 2a3
ANSWER:
yes; 3; trinomial
2.2y – 5 + 3y2
ANSWER:
yes; 2; trinomial
3.3x2
ANSWER:
yes; 2; monomial
4.
ANSWER:
No; a monomial cannot have a variable in the
denominator.
5.5m2p3 + 6
ANSWER:
yes; 5; binomial
6.5q–4 + 6q
ANSWER:
No; , and a monomial cannot have a
variable in the denominator.
Write each polynomial in standard form. Identify
the leading coefficient.
7.–4d4 + 1 – d2
ANSWER:
–4d4 – d2 + 1; –4
8.2x5 – 12 + 3x
ANSWER:
2x5 + 3x – 12 ; 2
9.4z – 2z2 – 5z4
ANSWER:
–5z4 – 2z2+4z; –5
10.2a + 4a3 – 5a2 – 1
ANSWER:
4a3– 5a2+2a– 1, 4
Find each sum or difference.
11.(6x3 − 4) + (−2x3 + 9)
ANSWER:
4x3 + 5
12.(g3 − 2g2 + 5g + 6) − (g2 + 2g)
ANSWER:
g3 − 3g2 + 3g + 6
13.(4 + 2a2 − 2a) − (3a2 − 8a + 7)
ANSWER:
−a2 + 6a − 3
14.(8y − 4y2) + (3y − 9y2)
ANSWER:
−13y2 + 11y
15.(−4z3 − 2z + 8) − (4z3 + 3z2 − 5)
ANSWER:
−8z3 − 3z2 − 2z + 13
16.(−3d2 − 8 + 2d) + (4d − 12 + d2)
ANSWER:
−2d2 + 6d − 20
17.(y + 5) + (2y + 4y2 – 2)
ANSWER:
4y2 + 3y + 3
18.(3n3 − 5n + n2) − (−8n2 + 3n3)
ANSWER:
9n2 − 5n
19.CCSS SENSE-MAKING The total number of
students T who traveled for spring break consists of
two groups: students who flew to their destinations F
and students who drove to their destination D. The
number (in thousands) of students who flew and the
total number of students who flew or drove can be
modeled by the following equations, where n is the
number of years since 1995.
T = 14n + 21
F = 8n + 7
a. Write an equation that models the number of
students who drove to their destination for this time
period.
b. Predict the number of students who will drive to
their destination in 2012.
c. How many students will drive or fly to their
destination in 2015?
ANSWER:
a.D(n) = 6n + 14
b.116,000students
c. 301,000 students
Determine whether each expression is a
polynomial. If it is a polynomial, find the degree
and determine whether it is a monomial,
binomial, or trinomial.
20.
ANSWER:
No; a monomial cannot have a variable in the
denominator.
21.
ANSWER:
yes; 0; monomial
22.c4 – 2c2 + 1
ANSWER:
yes; 4; trinomial
23.d + 3dc
ANSWER:
No; the exponent is a variable.
24.a – a2
ANSWER:
yes; 2; binomial
25.5n3 + nq3
ANSWER:
yes; 4; binomial
Write each polynomial in standard form. Identify
the leading coefficient.
26.5x2 – 2 + 3x
ANSWER:
5x2 + 3x – 2; 5
27.8y + 7y3
ANSWER:
7y3 + 8y; 7
28.4 – 3c – 5c2
ANSWER:
–5c2 – 3c + 4; –5
29.–y3 + 3y – 3y2 + 2
ANSWER:
–y3 – 3y2 + 3y + 2; –1
30.11t + 2t2 – 3 + t5
ANSWER:
t5 + 2t2 + 11t – 3; 1
31.2 + r – r3
ANSWER:
–r3 + r + 2; –1
32.
ANSWER:
33.–9b2 + 10b – b6
ANSWER:
–b6 – 9b2 + 10b; –1
Find each sum or difference.
34.(2c2 + 6c + 4) + (5c – 7)
ANSWER:
7c2 + 6c – 3
35.(2x + 3x2) − (7 − 8x2)
ANSWER:
11x2 + 2x − 7
36.(3c3 − c + 11) − (c2 + 2c + 8)
ANSWER:
3c3 − c2 − 3c + 3
37.(z2 + z) + (z2 − 11)
ANSWER:
2z2 + z − 11
38.(2x − 2y + 1) − (3y + 4x)
ANSWER:
−2x − 5y + 1
39.(4a − 5b2 + 3) + (6 − 2a + 3b2)
ANSWER:
−2b2 + 2a + 9
40.(x2y − 3x2 + y) + (3y − 2x2y)
ANSWER:
−x2y − 3x2 + 4y
41.(−8xy + 3x2 − 5y) + (4x2 − 2y + 6xy)
ANSWER:
7x2 − 2xy − 7y
42.(5n − 2p2 + 2np) − (4p2 + 4n)
ANSWER:
−6p2 + 2np + n
43.(4rxt − 8r2x + x2) − (6rx2 + 5rxt − 2x2)
ANSWER:
3x2 − rxt − 8r2x − 6rx2
44.PETS From 1999 through 2009, the number of dogs
D and the number of cats C (in hundreds) adopted
from animal shelters in the United States are
modeled by the equations D = 2n + 3 and C = n + 4,
where n is the number of years since 1999.
a. Write an equation that models the total number T
of dogs and cats adopted in hundreds for this time
period.
b. If this trend continues, how many dogs and cats
will be adopted in 2013?
ANSWER:
a. T(n) = 3n + 7
b. 4900 dogs and cats
Classify each polynomial according to its degree
and number of terms.
45.4x – 3x2 + 5
ANSWER:
quadratic trinomial
46.11z3
ANSWER:
cubic monomial
47.9 + y4
ANSWER:
quartic binomial
48.3x3 – 7
ANSWER:
cubic binomial
49.–2x5 – x2 + 5x – 8
ANSWER:
quintic polynomial
50.10t – 4t2 + 6t3
ANSWER:
cubic trinomial
51.ENROLLMENT In a rapidly growing
school system, the numbers (in hundreds) of
total students N and K-5 students P
enrolled from 2000 to 2009 are modeled
by the equations N = 1.25t2 – t + 7.5 and
P = 0.7t2 – 0.95t + 3.8, where t is the
number of years since 2000.
a. Write an equation modeling the number of 6-12
students S enrolled for this time period.
b. How many 6-12 students were enrolled in the
school system in 2007?
ANSWER:
a.
b. 3030
52.CCSSREASONING The perimeter of the figure
shown is represented by the expression 3x2 − 7x + 2.
Write a polynomial that represents the measure of
the third side.
ANSWER:
4x
53.GEOMETRY Consider the rectangle.
a. What does (4x2 + 2x – 1)(2x2 – x + 3) represent?
b. What does 2(4x2 + 2x – 1) + 2(2x2 – x + 3)
represent?
ANSWER:
a.theareaoftherectangle
b. the perimeter of the rectangle
Find each sum or difference.
54.(4x + 2y − 6z) + (5y − 2z + 7x) + (−9z − 2x − 3y)
ANSWER:
9x + 4y − 17z
55.(5a2 − 4) + (a2 − 2a + 12) + (4a2 − 6a + 8)
ANSWER:
10a2 − 8a + 16
56.(3c2 − 7) + (4c + 7) − (c2 + 5c − 8)
ANSWER:
2c2 − c + 8
57.(3n3 + 3n − 10) − (4n2 − 5n) + (4n3 − 3n2 − 9n + 4)
ANSWER:
7n3 − 7n2 − n − 6
58.FOOTBALL The National Football League is
divided into two conferences, the American A and
the National N. From 2002 through 2009, the total
attendance T (in thousands) for both conferences and
for the American Conference games are modeled by
the following equations, where x is the number of
years since 2002.
T = –0.69x3 + 55.83x2 + 643.31x + 10,538
A = –3.78x3 + 58.96x2 + 265.96x + 5257
Determine how many people attended National
Conference football games in 2009.
ANSWER:
8,829,000 people
59.CARRENTAL The cost to rent a car for a day is
$15 plus $0.15 for each mile driven.
a. Write a polynomial that represents the cost of
renting a car for m miles.
b. If a car is driven 145 miles, how much would it
cost to rent?
c. If a car is driven 105 miles each day for four
days, how much would it cost to rent a car?
d. If a car is driven 220 miles each day for seven
days, how much would it cost to rent a car?
ANSWER:
a. 15 + 0.15m
b. $36.75
c. $123
d. $336
60.MULTIPLE REPRESENTATIONS In this
problem, you will explore perimeter and area.
a. Geometric Draw three rectangles that each have
a perimeter of 400 feet.
b. Tabular Record the width and length of each
rectangle in a table like the one shown below. Find
the area of each rectangle.
c. Graphical On a coordinate system, graph the area
of rectangle 4 in terms of the length, x. Use the
graph to determine the largest area possible.
d. Analytical Determine the length and width that
produce the largest area.
ANSWER:
a.
b.
c.
d. The length and width of the rectangle must be 100
feet each to have the largest area.
61.CCSSCRITIQUE Cheyenne and Sebastian are
finding (2x2 − x) − (3x + 3x2 − 2). Is either of them
correct? Explain your reasoning.
ANSWER:
Neither; neither of them found the additive inverse
correctly. All terms should be multiplied by −1.
62.REASONING Determine whether each of the
following statements is true or false . Explain your
reasoning.
a. A binomial can have a degree of zero.
b. The order in which polynomials are subtracted
does not matter.
ANSWER:
a. False; sample answer: a binomial must have at
least one monomial term with degree greater than
zero.
b. False; sample answer: (2x – 3) – (4x – 3) = –2x,
but (4x – 3) – (2x – 3) = 2x
63.CHALLENGE Write a polynomial that represents
the sum of an odd integer 2n + 1 and the next two
consecutive odd integers.
ANSWER:
6n + 9
64.WRITING IN MATH Why would you add or
subtract equations that represent real-world
situations? Explain.
ANSWER:
Sample answer: When you add or subtract two or
more polynomial equations, like terms are combined,
which reduces the number of terms in the resulting
equation. This could help minimize the number of
operations performed when using the equations.
65.WRITINGINMATH Describe how to add and
subtract polynomials using both the vertical and
horizontalformats.
ANSWER:
Sample answer: To add polynomials in a horizontal
format, you combine like terms. For the vertical
format, you write the polynomials in standard form,
align like terms in columns, and combine like terms.
To subtract polynomials in a horizontal format you
find the additive inverse of the polynomial you are
subtracting, and then combine like terms. For the
vertical format, you write the polynomials in standard
form, align like terms in columns, and subtract by
adding the additive inverse.
66.Three consecutive integers can be represented by x,
x + 1, and x + 2. What is the sum of these three
integers?
A x(x + 1)(x + 2)
B x3 + 3
C 3x + 3
D x + 3
ANSWER:
C
67.SHORTRESPONSE What is the perimeter of a
square with sides that measure 2x + 3 units?
ANSWER:
8x + 12 units
68.Jim cuts a board in the shape of a regular hexagon
and pounds in a nail at each vertex, as shown. How
many rubber bands will he need to stretch a rubber
band across every possible pair of nails?
F 15
G 14
H 12
J 9
ANSWER:
F
69.Which ordered pair is in the solution set of the
system of inequalities shown in the graph?
A (−3, 0)
B (0, −3)
C (5, 0)
D (0, 5)
ANSWER:
C
70.COMPUTERS A computer technician charges by
the hour to fix and repair computer equipment. The
total cost of the technician for one hour is $75, for
two hours is $125, for three hours is $175, for four
hours is $225, and so on. Write a recursive formula
for the sequence.
ANSWER:
Determine whether each sequence is
arithmetic, geometric, or neither. Explain.
71.8, –32, 128, –512, ...
ANSWER:
Geometric; the common ratio is –4.
72.25, 8, –9, –26, ...
ANSWER:
Arithmetic; the common difference is –17.
73.
ANSWER:
Neither; there is no common ratio or difference.
74.43, 52, 61, 70, ...
ANSWER:
Arithmetic; the common difference is 9.
75.–27, –16, –5, 6, ...
ANSWER:
Arithmetic; the common difference is 11.
76.200, 100, 50, 25, …
ANSWER:
Geometric; the common ratio is .
77.JOBS Kimi received an offer for a new job. She
wants to compare the offer with her current job.
What is total amount of sales that Kimi must get
each month to make the same income at either job?
ANSWER:
$80,000
Determine whether each sequence is an
arithmetic sequence. If it is, state the common
difference.
78.24, 16, 8, 0, …
ANSWER:
yes; −8
79. , 13, 26, …
ANSWER:
no
80.7, 6, 5, 4, …
ANSWER:
yes; −1
81.10, 12, 15, 18, …
ANSWER:
no
82.−15, −11, −7, −3, …
ANSWER:
yes; 4
83.−0.3, 0.2, 0.7, 1.2, …
ANSWER:
yes; 0.5
Simplify.
84.t(t5)(t7)
ANSWER:
85.n3(n2)(−2n3)
ANSWER:
−2n8
86.(5t5v2)(10t3v4)
ANSWER:
50t8v6
87.(−8u4z5)(5uz4)
ANSWER:
−40u5z9
88.[(3)2]3
ANSWER:
729
89.[(2)3]2
ANSWER:
64
90.(2m4k3)2(−3mk2)3
ANSWER:
−108m11k12
91.(6xy2)2(2x2y2z2)3
ANSWER:
288x8y10z6
Determine whether each expression is a
polynomial. If it is a polynomial, find the degree
and determine whether it is a monomial,
binomial, or trinomial.
1.7ab + 6b2 – 2a3
ANSWER:
yes; 3; trinomial
2.2y – 5 + 3y2
ANSWER:
yes; 2; trinomial
3.3x2
ANSWER:
yes; 2; monomial
4.
ANSWER:
No; a monomial cannot have a variable in the
denominator.
5.5m2p3 + 6
ANSWER:
yes; 5; binomial
6.5q–4 + 6q
ANSWER:
No; , and a monomial cannot have a
variable in the denominator.
Write each polynomial in standard form. Identify
the leading coefficient.
7.–4d4 + 1 – d2
ANSWER:
–4d4 – d2 + 1; –4
8.2x5 – 12 + 3x
ANSWER:
2x5 + 3x – 12 ; 2
9.4z – 2z2 – 5z4
ANSWER:
–5z4 – 2z2+4z; –5
10.2a + 4a3 – 5a2 – 1
ANSWER:
4a3– 5a2+2a– 1, 4
Find each sum or difference.
11.(6x3 − 4) + (−2x3 + 9)
ANSWER:
4x3 + 5
12.(g3 − 2g2 + 5g + 6) − (g2 + 2g)
ANSWER:
g3 − 3g2 + 3g + 6
13.(4 + 2a2 − 2a) − (3a2 − 8a + 7)
ANSWER:
−a2 + 6a − 3
14.(8y − 4y2) + (3y − 9y2)
ANSWER:
−13y2 + 11y
15.(−4z3 − 2z + 8) − (4z3 + 3z2 − 5)
ANSWER:
−8z3 − 3z2 − 2z + 13
16.(−3d2 − 8 + 2d) + (4d − 12 + d2)
ANSWER:
−2d2 + 6d − 20
17.(y + 5) + (2y + 4y2 – 2)
ANSWER:
4y2 + 3y + 3
18.(3n3 − 5n + n2) − (−8n2 + 3n3)
ANSWER:
9n2 − 5n
19.CCSS SENSE-MAKING The total number of
students T who traveled for spring break consists of
two groups: students who flew to their destinations F
and students who drove to their destination D. The
number (in thousands) of students who flew and the
total number of students who flew or drove can be
modeled by the following equations, where n is the
number of years since 1995.
T = 14n + 21
F = 8n + 7
a. Write an equation that models the number of
students who drove to their destination for this time
period.
b. Predict the number of students who will drive to
their destination in 2012.
c. How many students will drive or fly to their
destination in 2015?
ANSWER:
a.D(n) = 6n + 14
b.116,000students
c. 301,000 students
Determine whether each expression is a
polynomial. If it is a polynomial, find the degree
and determine whether it is a monomial,
binomial, or trinomial.
20.
ANSWER:
No; a monomial cannot have a variable in the
denominator.
21.
ANSWER:
yes; 0; monomial
22.c4 – 2c2 + 1
ANSWER:
yes; 4; trinomial
23.d + 3dc
ANSWER:
No; the exponent is a variable.
24.a – a2
ANSWER:
yes; 2; binomial
25.5n3 + nq3
ANSWER:
yes; 4; binomial
Write each polynomial in standard form. Identify
the leading coefficient.
26.5x2 – 2 + 3x
ANSWER:
5x2 + 3x – 2; 5
27.8y + 7y3
ANSWER:
7y3 + 8y; 7
28.4 – 3c – 5c2
ANSWER:
–5c2 – 3c + 4; –5
29.–y3 + 3y – 3y2 + 2
ANSWER:
–y3 – 3y2 + 3y + 2; –1
30.11t + 2t2 – 3 + t5
ANSWER:
t5 + 2t2 + 11t – 3; 1
31.2 + r – r3
ANSWER:
–r3 + r + 2; –1
32.
ANSWER:
33.–9b2 + 10b – b6
ANSWER:
–b6 – 9b2 + 10b; –1
Find each sum or difference.
34.(2c2 + 6c + 4) + (5c – 7)
ANSWER:
7c2 + 6c – 3
35.(2x + 3x2) − (7 − 8x2)
ANSWER:
11x2 + 2x − 7
36.(3c3 − c + 11) − (c2 + 2c + 8)
ANSWER:
3c3 − c2 − 3c + 3
37.(z2 + z) + (z2 − 11)
ANSWER:
2z2 + z − 11
38.(2x − 2y + 1) − (3y + 4x)
ANSWER:
−2x − 5y + 1
39.(4a − 5b2 + 3) + (6 − 2a + 3b2)
ANSWER:
−2b2 + 2a + 9
40.(x2y − 3x2 + y) + (3y − 2x2y)
ANSWER:
−x2y − 3x2 + 4y
41.(−8xy + 3x2 − 5y) + (4x2 − 2y + 6xy)
ANSWER:
7x2 − 2xy − 7y
42.(5n − 2p2 + 2np) − (4p2 + 4n)
ANSWER:
−6p2 + 2np + n
43.(4rxt − 8r2x + x2) − (6rx2 + 5rxt − 2x2)
ANSWER:
3x2 − rxt − 8r2x − 6rx2
44.PETS From 1999 through 2009, the number of dogs
D and the number of cats C (in hundreds) adopted
from animal shelters in the United States are
modeled by the equations D = 2n + 3 and C = n + 4,
where n is the number of years since 1999.
a. Write an equation that models the total number T
of dogs and cats adopted in hundreds for this time
period.
b. If this trend continues, how many dogs and cats
will be adopted in 2013?
ANSWER:
a. T(n) = 3n + 7
b. 4900 dogs and cats
Classify each polynomial according to its degree
and number of terms.
45.4x – 3x2 + 5
ANSWER:
quadratic trinomial
46.11z3
ANSWER:
cubic monomial
47.9 + y4
ANSWER:
quartic binomial
48.3x3 – 7
ANSWER:
cubic binomial
49.–2x5 – x2 + 5x – 8
ANSWER:
quintic polynomial
50.10t – 4t2 + 6t3
ANSWER:
cubic trinomial
51.ENROLLMENT In a rapidly growing
school system, the numbers (in hundreds) of
total students N and K-5 students P
enrolled from 2000 to 2009 are modeled
by the equations N = 1.25t2 – t + 7.5 and
P = 0.7t2 – 0.95t + 3.8, where t is the
number of years since 2000.
a. Write an equation modeling the number of 6-12
students S enrolled for this time period.
b. How many 6-12 students were enrolled in the
school system in 2007?
ANSWER:
a.
b. 3030
52.CCSSREASONING The perimeter of the figure
shown is represented by the expression 3x2 − 7x + 2.
Write a polynomial that represents the measure of
the third side.
ANSWER:
4x
53.GEOMETRY Consider the rectangle.
a. What does (4x2 + 2x – 1)(2x2 – x + 3) represent?
b. What does 2(4x2 + 2x – 1) + 2(2x2 – x + 3)
represent?
ANSWER:
a.theareaoftherectangle
b. the perimeter of the rectangle
Find each sum or difference.
54.(4x + 2y − 6z) + (5y − 2z + 7x) + (−9z − 2x − 3y)
ANSWER:
9x + 4y − 17z
55.(5a2 − 4) + (a2 − 2a + 12) + (4a2 − 6a + 8)
ANSWER:
10a2 − 8a + 16
56.(3c2 − 7) + (4c + 7) − (c2 + 5c − 8)
ANSWER:
2c2 − c + 8
57.(3n3 + 3n − 10) − (4n2 − 5n) + (4n3 − 3n2 − 9n + 4)
ANSWER:
7n3 − 7n2 − n − 6
58.FOOTBALL The National Football League is
divided into two conferences, the American A and
the National N. From 2002 through 2009, the total
attendance T (in thousands) for both conferences and
for the American Conference games are modeled by
the following equations, where x is the number of
years since 2002.
T = –0.69x3 + 55.83x2 + 643.31x + 10,538
A = –3.78x3 + 58.96x2 + 265.96x + 5257
Determine how many people attended National
Conference football games in 2009.
ANSWER:
8,829,000 people
59.CARRENTAL The cost to rent a car for a day is
$15 plus $0.15 for each mile driven.
a. Write a polynomial that represents the cost of
renting a car for m miles.
b. If a car is driven 145 miles, how much would it
cost to rent?
c. If a car is driven 105 miles each day for four
days, how much would it cost to rent a car?
d. If a car is driven 220 miles each day for seven
days, how much would it cost to rent a car?
ANSWER:
a. 15 + 0.15m
b. $36.75
c. $123
d. $336
60.MULTIPLE REPRESENTATIONS In this
problem, you will explore perimeter and area.
a. Geometric Draw three rectangles that each have
a perimeter of 400 feet.
b. Tabular Record the width and length of each
rectangle in a table like the one shown below. Find
the area of each rectangle.
c. Graphical On a coordinate system, graph the area
of rectangle 4 in terms of the length, x. Use the
graph to determine the largest area possible.
d. Analytical Determine the length and width that
produce the largest area.
ANSWER:
a.
b.
c.
d. The length and width of the rectangle must be 100
feet each to have the largest area.
61.CCSSCRITIQUE Cheyenne and Sebastian are
finding (2x2 − x) − (3x + 3x2 − 2). Is either of them
correct? Explain your reasoning.
ANSWER:
Neither; neither of them found the additive inverse
correctly. All terms should be multiplied by −1.
62.REASONING Determine whether each of the
following statements is true or false . Explain your
reasoning.
a. A binomial can have a degree of zero.
b. The order in which polynomials are subtracted
does not matter.
ANSWER:
a. False; sample answer: a binomial must have at
least one monomial term with degree greater than
zero.
b. False; sample answer: (2x – 3) – (4x – 3) = –2x,
but (4x – 3) – (2x – 3) = 2x
63.CHALLENGE Write a polynomial that represents
the sum of an odd integer 2n + 1 and the next two
consecutive odd integers.
ANSWER:
6n + 9
64.WRITING IN MATH Why would you add or
subtract equations that represent real-world
situations? Explain.
ANSWER:
Sample answer: When you add or subtract two or
more polynomial equations, like terms are combined,
which reduces the number of terms in the resulting
equation. This could help minimize the number of
operations performed when using the equations.
65.WRITINGINMATH Describe how to add and
subtract polynomials using both the vertical and
horizontalformats.
ANSWER:
Sample answer: To add polynomials in a horizontal
format, you combine like terms. For the vertical
format, you write the polynomials in standard form,
align like terms in columns, and combine like terms.
To subtract polynomials in a horizontal format you
find the additive inverse of the polynomial you are
subtracting, and then combine like terms. For the
vertical format, you write the polynomials in standard
form, align like terms in columns, and subtract by
adding the additive inverse.
66.Three consecutive integers can be represented by x,
x + 1, and x + 2. What is the sum of these three
integers?
A x(x + 1)(x + 2)
B x3 + 3
C 3x + 3
D x + 3
ANSWER:
C
67.SHORTRESPONSE What is the perimeter of a
square with sides that measure 2x + 3 units?
ANSWER:
8x + 12 units
68.Jim cuts a board in the shape of a regular hexagon
and pounds in a nail at each vertex, as shown. How
many rubber bands will he need to stretch a rubber
band across every possible pair of nails?
F 15
G 14
H 12
J 9
ANSWER:
F
69.Which ordered pair is in the solution set of the
system of inequalities shown in the graph?
A (−3, 0)
B (0, −3)
C (5, 0)
D (0, 5)
ANSWER:
C
70.COMPUTERS A computer technician charges by
the hour to fix and repair computer equipment. The
total cost of the technician for one hour is $75, for
two hours is $125, for three hours is $175, for four
hours is $225, and so on. Write a recursive formula
for the sequence.
ANSWER:
Determine whether each sequence is
arithmetic, geometric, or neither. Explain.
71.8, –32, 128, –512, ...
ANSWER:
Geometric; the common ratio is –4.
72.25, 8, –9, –26, ...
ANSWER:
Arithmetic; the common difference is –17.
73.
ANSWER:
Neither; there is no common ratio or difference.
74.43, 52, 61, 70, ...
ANSWER:
Arithmetic; the common difference is 9.
75.–27, –16, –5, 6, ...
ANSWER:
Arithmetic; the common difference is 11.
76.200, 100, 50, 25, …
ANSWER:
Geometric; the common ratio is .
77.JOBS Kimi received an offer for a new job. She
wants to compare the offer with her current job.
What is total amount of sales that Kimi must get
each month to make the same income at either job?
ANSWER:
$80,000
Determine whether each sequence is an
arithmetic sequence. If it is, state the common
difference.
78.24, 16, 8, 0, …
ANSWER:
yes; −8
79. , 13, 26, …
ANSWER:
no
80.7, 6, 5, 4, …
ANSWER:
yes; −1
81.10, 12, 15, 18, …
ANSWER:
no
82.−15, −11, −7, −3, …
ANSWER:
yes; 4
83.−0.3, 0.2, 0.7, 1.2, …
ANSWER:
yes; 0.5
Simplify.
84.t(t5)(t7)
ANSWER:
85.n3(n2)(−2n3)
ANSWER:
−2n8
86.(5t5v2)(10t3v4)
ANSWER:
50t8v6
87.(−8u4z5)(5uz4)
ANSWER:
−40u5z9
88.[(3)2]3
ANSWER:
729
89.[(2)3]2
ANSWER:
64
90.(2m4k3)2(−3mk2)3
ANSWER:
−108m11k12
91.(6xy2)2(2x2y2z2)3
ANSWER:
288x8y10z6
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8-1 Adding and Subtracting Polynomials
