Deck 5: Polynomials and Polynomial Functions

Question 1

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $- 1 - 3 x ^ { 4 } + 7 x ^ { 5 }$

A)descending order, degree 5
B) $7 x ^ { 5 } - 3 x ^ { 4 } - 1 , \text { degree } 9$
C) $$7 x ^ { 5 } - 3 x ^ { 4 } - 1 \text {, degree } 5$$
D)descending order, degree 10

Answer 1

$$7 x ^ { 5 } - 3 x ^ { 4 } - 1 \text {, degree } 5$$

Question 2

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $9 s ^ { 4 } - 7 s - 7$

A)monomial
B)trinomial
C)not polynomial, no variable in last term
D)binomial

Answer 2

trinomial

Question 3

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $5 y ^ { 4 } + 5 x ^ { 2 } + 6 x + 19 x ^ { 3 }$

A) $19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } , \text { degree } 10$
B) $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 10$
C) $5 y ^ { 4 } + 19 x ^ { 3 } + 5 x ^ { 2 } + 6 x \text {, degree } 4$
D) $$19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } \text {, degree } 4$$

Answer 3

$$19 x ^ { 3 } + 5 x ^ { 2 } + 6 x + 5 y ^ { 4 } \text {, degree } 4$$

Question 4

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
-15x

A)monomial
B)binomial
C)not polynomial, no exponent on the variable
D)trinomial

Question 5

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $4 x ^ { 3 } + 5 x ^ { 2 } - 4 x ^ { - 4 }$

A)trinomial
B)polynomial
C)monomial
D)not polynomial, -4 exponent

Question 6

Give the degree of the polynomial and identify its leading coefficient.

- $- 9 x ^ { 3 } + 8 x ^ { 4 } - x ^ { 5 } + 12$

A)degree: 5; leading coefficient: -9
B)degree: 5; leading coefficient: -1
C)degree: 3; leading coefficient: -9
D)degree: 5; leading coefficient: 1

Question 7

Give the degree of the polynomial and identify its leading coefficient.

- $- 9 x ^ { 3 } - 8 x ^ { 4 } + 18 x ^ { 5 } + 12$

A)degree: 3; leading coefficient: 18
B)degree: 5; leading coefficient: -9
C)degree: 3; leading coefficient: -9
D)degree: 5; leading coefficient: 18

Question 8

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $- 10 y ^ { 4 } - 9$

A)monomial
B)binomial
C)trinomial
D)not polynomial, no variable in second term

Question 9

Give the degree of the polynomial and identify its leading coefficient.

- $8 x ^ { 3 } y ^ { 2 } - 7 x ^ { 5 } y ^ { 4 } + x ^ { 9 } y$

A)degree: 10; leading coefficient: 8
B)degree: 9; leading coefficient: -7
C)degree:9; leading coefficient: 8
D)degree: 10; leading coefficient: 1

Question 10

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.
7

A)not polynomial, no variables
B)monomial
C)binomial
D)trinomial

Question 11

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $3 x y ^ { 3 } - 2 x ^ { 2 } + 9 + 11 x ^ { 3 }$

A) $3 x y ^ { 3 } + 11 x ^ { 3 } - 2 x ^ { 2 } + 9 , \text { degree } 3$
B) $11 x ^ { 3 } - 2 x ^ { 2 } + 3 x y ^ { 3 } + 9 , \text { degree } 4$
C) $11 x ^ { 3 } - 2 x ^ { 2 } + 3 x y ^ { 3 } + 9 \text {, degree } 3$
D) $3 x y ^ { 3 } + 11 x ^ { 3 } - 2 x ^ { 2 } + 9 , \text { degree } 4$

Question 12

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $- 10 a ^ { 2 }$

A)monomial
B)trinomial
C)not polynomial, lacks other terms
D)binomial

Question 13

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $- 20 x ^ { 7 } + 9$

A) $9 - 20 x ^ { 7 } , \text { degree } 7$
B)descending order, degree 7
C)descending order, degree 8
D) $9 - 20 x ^ { 7 } , \text { degree } 8$

Question 14

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $6 y ^ { 5 } + 8 y ^ { 4 } - 6$

A)binomial
B)monomial
C)trinomial
D)not polynomial, no variable in last term

Question 15

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $x ^ { 4 / 3 } - x ^ { 6 } - 1$

A)trinomial
B)monomial
C)binomial
D)not polynomial, 4/3 exponent

Question 16

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $- 11 z + 6$

A)monomial
B)trinomial
C)not polynomial, no variable in second term
D)binomial

Question 17

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $- 10 x - 6$

A)descending order, degree 1
B)descending order, degree 0
C)-6 - 10x, degree 1
D)-6 - 10x, degree 2

Question 18

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $5 x - 6 x ^ { 3 } + 1$

A)descending order, degree 4
B)descending order, degree 5
C) $- 6 x ^ { 3 } + 5 x + 1 \text {, degree } 3$
D) $- 6 x ^ { 3 } + 5 x + 1 , \text { degree } 4$

Question 19

Write the polynomial in descending order of the variable x. If the polynomial is already in descending order, so state.
Give the degree of the polynomial.

- $- 8 x ^ { 3 } - 2 x ^ { 4 } + 8 x ^ { 5 } + 12$

A)descending order, degree 5
B)descending order, degree 12
C) $8 x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 } + 12 , \text { degree } 5$
D) $8 x ^ { 5 } - 2 x ^ { 4 } - 8 x ^ { 3 } + 12 , \text { degree } 13$

Question 20

Determine whether the expression is a polynomial. If the expression is a polynomial, state whether it is a monomial,
binomial, or trinomial. If the expression is not a polynomial, indicate why not.

- $- 20 y z + 6 z ^ { 2 }$

A)not polynomial, first term contains 2 different variables y and z
B)monomial
C)trinomial
D)binomial

Question 21

Solve the problem.

-The area of a circle of radius r is given by the polynomialal $$\pi r ^ { 2 },$$ , where π is an irrational number. Use 3.14 as an approximation of $\pi ,$ and find the area of a circle with radius 7 cm.

A) $147 \mathrm {~cm} ^ { 2 }$
B) $21.98 \mathrm {~cm} ^ { 2 }$
C) $153.86 \mathrm {~cm} ^ { 2 }$
D) $43.96 \mathrm {~cm} ^ { 2 }$

Question 22

Give the degree of the polynomial and identify its leading coefficient.

- $21 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

A)degree: 6; leading coefficient: 21
B)degree: 5; leading coefficient: 10
C)degree: 6; leading coefficient: -1
D)degree: 6; leading coefficient: 2

Question 23

Solve the problem.

-The number of different committees of 2 students where the 2 students are selected from a group of n students is given by $c ( n ) = \frac { 1 } { 2 } \left( n ^ { 2 } - n \right)$ n). How many different committees of 2 students can be selected from a group of 10
Students?

A)10
B)20
C)45
D)1

Question 24

Solve the problem.

-The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by $1.28 \mathrm { x } ^ { 2 } + 0.056 \mathrm { x }$ Find the stopping distance for a speed of 40 mph. Round to the nearest foot.

A)2041 ft
B)2 ft
C)2070 ft
D)2050 ft

Question 25

Evaluate the polynomial function at the given value.

-Find P(0.2)if P(x)= $0.2 x ^ { 2 }$ - 4.2x + 2.7

A)-0.049
B)1.868
C)-0.805
D)-1.868

Question 26

Solve the problem.

-When a coin is dropped from a cliff of height 1800 feet, the height h of the coin from the ground (in feet)t seconds after being dropped is given by h = $- 16 t ^ { 2 }$ + 1800. How high is the coin above the ground 9 seconds
After being dropped?

A)494 ft
B)518 ft
C)504 ft
D)538 ft

Question 27

Evaluate the polynomial function at the given value.

-Find P(4)if P(x)= $x ^ { 2 } + 2 x + 4$

A)16
B)24
C)22
D)28

Question 28

Evaluate the polynomial function at the given value.

-Findd P( $P ( - 5 ) \text { if } P ( x ) = 2 x ^ { 2 } - 9 x - 6$

A)-1
B)-11
C)89
D)-101

Question 29

Evaluate the polynomial function at the given value.

- $\text { Find } \mathrm { P } \left( \frac { 1 } { 2 } \right) \text { if } \mathrm { P } ( \mathrm { x } ) = - 2 \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 7$

A) $\frac { 5 } { 2 }$
B)9
C) $- \frac { 5 } { 2 }$
D)- 9

Question 30

Give the degree of the polynomial and identify its leading coefficient.

- $$\frac { 8 } { 15 } m ^ { 3 } n ^ { 2 } p ^ { 4 } - m ^ { 6 } p ^ { 2 } - \frac { 5 } { 13 } m n ^ { 3 } p ^ { 6 }$$

A) $- \frac { 5 } { 13 }$
B) $- \frac { 5 } { 13 }$ .
C) $\frac { 8 } { 15 }$
D) $\frac { 8 } { 15 }$ .

Question 31

Solve the problem.

-The position of an object moving in a straight line is given by $\mathrm { s } = 11 \mathrm { t } ^ { 2 } - 7 \mathrm { t },$ where s is in where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 15 seconds?

A)1410 meters
B)60 meters
C)900 meters
D)2370 meters

Question 32

Solve the problem.

-The volume of a sphere is a function of its radius, r, where $\mathrm { V } ( \mathrm { r } ) = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ . Find the volume of a sphere if its radius is 7 inches. Use 3.14 as an approximation to the value of π. Round to the nearest tenth if necessary.

A) $205.1 \mathrm { in. } ^ { 3 }$
B) $179.5 \mathrm { in. } ^ { 3 }$
C) $807.8 \text { in.} ^3$
D) $1436 \text { in.}^ 3$

Question 33

Evaluate the polynomial function at the given value.
Find P(-2)if P(x)= -9x - 8.

A)-26
B)10
C)-10
D)26

Question 34

Solve the problem.

-The number of ways that the first-, second-, and third-place winners in a singing competition can be selected from n finalists is given by $P ( n ) = n ^ { 3 } - 3 n ^ { 2 } + 2 n$ . If there are6 finalists, how many ways can the first-, second-,
And third-place winners be selected?

A)120
B)720
C)20
D)216

Question 35

Evaluate the polynomial function at the given value.

-Find P(-1)if P(x)= $x ^ { 2 } + 8$

A)49
B)1
C)9
D)7

Question 36

Evaluate the polynomial function at the given value.

-Find P(-2)if P(x)= $8 x ^ { 2 } - 2 x$

A)32
B)36
C)28
D)-12

Question 37

Give the degree of the polynomial and identify its leading coefficient.

- $- 9 x ^ { 4 } - 7 w ^ { 3 } + 2 w - 4 y ^ { 5 } + 4$

A)degree: 13; leading coefficient: -4
B)degree: 5; leading coefficient: -4
C)degree: 13; leading coefficient: -9
D)degree: 5; leading coefficient: -9

Question 38

Give the degree of the polynomial and identify its leading coefficient.

- $3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s$

A)degree: 5; leading coefficient: 3
B)degree: 4; leading coefficient: 1
C)degree: 5; leading coefficient: 15
D)degree: 4; leading coefficient: 3

Question 39

Solve the problem.
The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the polynomial equation C(x)= 0.6x + 27,000. Find the cost of producing 90,000 jars.

A)$27.60
B)$54,000
C)$81,000
D)$90,027

Question 40

Solve the problem.

-The volume of a cube is a function of its side, s, where $$V ( s ) = s ^ { 3 }$$ . Find the volume of a cube if its side is 9 centimeters.

A) $27 \mathrm {~cm} ^ { 3 }$
B) $27 \mathrm {~cm} ^ { 2 }$
C) $729 \mathrm {~cm} ^ { 2 }$
D) $729 \mathrm {~cm} ^ { 3 }$

Question 41

Simplify.

- $\left( x ^ { 2 } + 4 x - 8 \right) + ( 3 x - 6 )$

A) $3 x ^ { 2 } + 4 x - 14$
B) $3 x ^ { 2 } + 7 x - 14$
C) $x ^ { 2 } + 7 x - 14$
D) $- 7 x ^ { 2 }$

Question 42

Simplify.

-( $\left( 4 x ^ { 2 } - 2 x - 1 \right) - \left( 2 x ^ { 2 } + 6 x - 4 \right)$

A) $2 x ^ { 2 } + 4 x + 3$
B) $2 x ^ { 2 } - 8 x - 5$
C) $2 x ^ { 2 } - 8 x + 3$
D) $2 x ^ { 2 } + 4 x - 5$

Question 43

Simplify.

- $( 3 a - 2 b - 5 c ) - ( 9 a - 6 b - 7 c )$

A) $12 a - 8 b - 12 c$
B) $- 6 a - 8 b + 2 c$
C) $- 6 a + 4 b + 2 c$
D) $- 6 a + 4 b - 12 c$

Question 44

Solve the problem.

-A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } + 300 t$ . Find the height of the projectile at t = 8 seconds.

A)2400 ft
B)1376 ft
C)2272 ft
D)1476 ft

Question 45

Determine which of the graphs is the graph of the equation.

- $f ( x ) = 8 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 2$

A)
B)
C)
D)

Question 46

Determine which of the graphs is the graph of the equation.

- $f ( x ) = - 3 x ^ { 2 } + 3 x + 2$

A)
B)
C)
D)

Question 47

Determine which of the graphs is the graph of the equation.

- $f ( x ) = 4 x ^ { 2 } - 2 x - 1$

A)
B)
C)
D)

Question 48

Solve the problem.

-An object is thrown upward with an initial velocity of 20 feet per second from the top of a 588-foot building. The height of the object at any time t can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } + 20 t + 588$ F Find
The height of the object at t = 5 seconds.

A)-300 ft
B)288 ft
C)608 ft
D)208 ft

Question 49

Simplify.

- $\left( 7 x ^ { 2 } - x y - y ^ { 2 } \right) + \left( x ^ { 2 } + 6 x y - 5 y ^ { 2 } \right)$

A) $8 x ^ { 2 } + 5 x y + 4 y ^ { 2 }$
B) $8 x ^ { 2 } - 7 x y + 4 y ^ { 2 }$
C) $8 x ^ { 2 } + 5 x y - 6 y ^ { 2 }$
D) $8 x ^ { 2 } - 7 x y + 6 y ^ { 2 }$

Question 50

Solve the problem.

-The polynomial $- 0.3 \mathrm { t } ^ { 2 } + 10 \mathrm { t }$ describes the average number of digits that participants in a memorization experiment were able to recall after t minutes. Find the number of digits recalled after 9 minutes. Round to the
Nearest digit.

A)46 digits
B)66 digits
C)86 digits
D)106 digits

Question 51

Determine which of the graphs is the graph of the equation.

- $f ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 3$

A)
B)
C)
D)

Question 52

Solve the problem.

-Total profit is defined as total revenue minus total cost. R(x)is the revenue from the sale of x televisions and C(x)is the cost of producing x televisions.(x)is the cost of producing x televisions. $\text { If } R ( x ) = 240 x - 0.7 x ^ { 2 } \text { and } C ( x ) = 4000 + 0.6 x ^ { 2 } \text {, }$ find the profit from the
Sale of 80 televisions.

A)$22,560
B)$14,880
C)$6880
D)$14,560

Question 53

Simplify.

- $\left( 28 y ^ { 2 } + 4 \right) - \left( - 11 y ^ { 4 } - 14 y ^ { 2 } + 4 \right)$

A) $11 y ^ { 4 } + 42 y ^ { 2 } - 8$
B) $- 11 y ^ { 4 } + 14 y ^ { 2 } + 8$
C) $53 y ^ { 6 }$
D) $11 y ^ { 4 } + 42 y ^ { 2 }$

Question 54

Simplify.

- $\left( 5 m + 10 m ^ { 3 } \right) - \left( - 8 - 3 m - 3 m ^ { 3 } \right)$

A) $13 m ^ { 3 } + 8 m + 8$
B) $$7 m ^ { 3 } + 8 m - 8$$
C) $7 m ^ { 3 } + 8 m + 8$
D) $13 m ^ { 3 } + 8 m - 8$

Question 55

Simplify.

- $( 12 y + 9 ) + \left( 11 y ^ { 2 } - 6 y + 9 \right)$

A) $11 y ^ { 2 } + 18 y - 18$
B) $29 y ^ { 6 }$
C) $11 y ^ { 2 } - 6 y + 18$
D) $11 y ^ { 2 } + 6 y + 18$

Question 56

Simplify.

- $\left( 12 x ^ { 2 } y - 6 x y + 9 \right) + \left( - 11 x ^ { 2 } y + 8 x y - 5 \right)$

A) $- x ^ { 2 } y - 14 x y + 14$
B) $23 x ^ { 2 } y + 14 x y + 14$
C) $x ^ { 2 } y + 2 x y + 4$
D) $2 x ^ { 3 } y ^ { 2 } + 4$

Question 57

Simplify.

- $6 z - ( 17 - 2 z )$

A)8z + 17
B) $4 z + 17$
C) $8 z - 17$
D) $4 z - 17$

Question 58

Solve the problem.

-Computer sales in the United States have increased since 1992. The function $f ( x ) = 0.058 x ^ { 2 } + 0.69 x + 4.8$ can be used to approximate the number of computer sales during the years 1990-2000 where x is the number of years
After 1990 and f(x)is the computer sales (in millions). Approximate the number of computers sold in 1996.
Round the answer to the nearest tenth of a million.

A)9.7 million
B)11 million
C)9.3 million
D)12.5 million

Question 59

Simplify.

-( $\left( 4 x ^ { 2 } + 7 x + 7 \right) - \left( - 10 x ^ { 2 } + 1 \right)$

A) $14 x ^ { 2 } + 7 x + 6$
B) $14 x ^ { 2 } + 6 x + 7$
C) $- 6 x ^ { 2 } + 6 x + 7$
D) $- 6 x ^ { 2 } + 7 x + 6$

Question 60

Simplify.

- $( 18 y + 5 ) - \left( - 14 y ^ { 2 } - 9 y + 5 \right)$

A) $14 y ^ { 2 } + 27 y - 10$
B) $14 y ^ { 2 } + 27 y$
C) $- 14 y ^ { 2 } + 9 y + 10$
D) $14 y ^ { 2 } + 9 y$

Question 61

Find an expression for the perimeter of the figure.

-
$~~~~~~x^{2}-x+17$

A) $x ^ { 2 } + 5 x + 30$
B) $2 x ^ { 2 } + 10 x + 30$
C) $2 x ^ { 2 } + 10 x + 60$
D) $2 x ^ { 2 } + 14 x + 60$

Question 62

Simplify.

- $\left[ \left( 1.9 x ^ { 3 } + 7.4 x ^ { 2 } + 4.7 \right) + ( 6.5 x - 2.8 ) \right] - \left( 3.9 x ^ { 2 } - x - 9.6 \right)$

A) $1.9 x ^ { 3 } + 11.3 x ^ { 2 } + 5.5 x - 7.7$
B) $1.9 x ^ { 3 } + 3.5 x ^ { 2 } + 6.5 x + 11.5$
C) $1.9 x ^ { 3 } + 3.5 x ^ { 2 } + 7.5 x + 11.5$
D) $12.9 x ^ { 6 } + 11.5$

Question 63

Find an expression for the perimeter of the figure.

-
$x ^ { 2 } - 9 x + 1$

A) $x ^ { 4 } - 18 x ^ { 2 } + 2$
B) $x ^ { 2 } - 18 x + 2$
C) $x ^ { 4 } - 36 x ^ { 2 } + 4$
D) $4 x ^ { 2 } - 36 x + 4$

Question 64

Find an expression for the perimeter of the figure.

-

A) $4 x ^ { 2 } + 8 x + 21$
B) $3 x ^ { 2 } + 8 x + 18$
C) $3 x ^ { 2 } + 9 x + 21$
D) $4 x ^ { 2 } + 9 x + 21$

Question 65

Multiply.

- $\left( - 7 x ^ { 5 } y \right) \left( - 4 x ^ { 6 } y ^ { 3 } \right)$

A) $- 11 x ^ { 11 } y ^ { 3 }$
B) $28 x ^ { 30 } y ^ { 3 }$
C) $- 28 x ^ { 11 } y ^ { 3 }$
D) $28 x ^ { 11 } y ^ { 4 }$

Question 66

Simplify. Assume that all exponents represent natural numbers.

- $\left( 8 x ^ { 2 r } - x ^ { r } - 1 \right) + \left( x ^ { 2 r } + 5 x ^ { r } + 3 \right)$

A) $9 x ^ { 4 r } + 6 x ^ { 2 r } + 4$
B) $7 x ^ { 4 r } - 6 x ^ { 2 r } - 4$
C) $9 x ^ { 2 r } + 4 x ^ { r } + 2$
D) $8 x ^ { 2 r } + 5 x ^ { r } + 3$

Question 67

Simplify.
Subtract (x - 2)from (8x - 4)

A)8x - 2
B)7x - 6
C)8x - 6
D)7x - 2

Question 68

Simplify.

- $\left( 2.5 x ^ { 3 } - 5.2 x ^ { 2 } - 4 \right) - \left( 8.8 x ^ { 3 } - 3.2 x ^ { 2 } + 3 \right)$

A) $- 6.3 x ^ { 3 } - 2 x ^ { 2 } - 7$
B) $11.3 x ^ { 3 } - 2 x ^ { 2 } - 7$
C) $- 6.3 x ^ { 3 } - 2 x ^ { 2 } + 7$
D) $- 6.3 x ^ { 3 } - 8.4 x ^ { 2 } - 7$

Question 69

Simplify.

- $\left( 5 m ^ { 2 } + 9 m n - 6 n ^ { 2 } \right) - \left( 9 m ^ { 2 } + 4 m n - 9 n ^ { 2 } \right)$

A) $- 4 m ^ { 2 } + 5 m n - 15 n ^ { 2 }$
B) $- 4 m ^ { 2 } + 13 m n + 3 n ^ { 2 }$
C) $- 4 m ^ { 2 } + 5 m n + 3 n ^ { 2 }$
D) $14 m ^ { 2 } + 13 m n - 15 n ^ { 2 }$

Question 70

Simplify.

-Subtract ( $\left( 12 a ^ { 2 } b - 9 a b \right)$ from ( $\left( 10 a ^ { 2 } b - 13 a b \right)$

A) $- 2 a ^ { 2 } b - 4 a b$
B) $- 2 a ^ { 2 } b - 22 a b$
C) $22 a ^ { 2 } b - 22 a b$
D) $22 a ^ { 2 } b - 4 a b$

Question 71

Simplify. Assume that all exponents represent natural numbers.

- $\left( 3 y ^ { 2 n } + 9 y ^ { n } - 1 \right) - \left( 4 y ^ { 2 n } + 3 y ^ { n } - 9 \right)$

A) $y ^ { 2 n } + 6 y ^ { n } + 8$
B) $- y ^ { 2 n } - 6 y ^ { n } - 10$
C) $- y ^ { 2 n } + 6 y ^ { n } + 8$
D) $- y ^ { 2 n } + 6 y ^ { n } - 10$

Question 72

Find an expression for the perimeter of the figure.

-

A) $2 x ^ { 2 } + 14 x + 36$
B) $x ^ { 2 } + 12 x + 42$
C) $2 x ^ { 2 } + 12 x + 42$
D) $2 x ^ { 2 } + 14 x + 42$

Question 73

Simplify.

-Subtract $- 7 s ^ { 2 } - 3 s + 1 . \text { from } - s ^ { 2 } - 7 s + 5$

A) $6 s ^ { 2 } - 4 s + 4$
B) $6 s ^ { 2 } + 4 s + 4$
C) $- 8 s ^ { 2 } - 10 s + 6$
D) $$8 s ^ { 2 } - 4 s + 6$$

Question 74

Simplify.

-Add $4 x ^ { 2 } y - 7 x y + 3$ and $- 3 x ^ { 2 } y + 10 x y - 8$

A) $- x ^ { 2 } y - 17 x y + 11$
B) $7 x ^ { 2 } y + 17 x y + 11$
C) $x ^ { 2 } y + 3 x y - 5$
D) $3 x ^ { 3 } y ^ { 2 } - 5$

Question 75

Simplify.

- $\left( 3 w ^ { 2 } - 6 w \right) - \left[ \left( w ^ { 2 } + 5 w \right) - \left( 5 w ^ { 2 } - 2 w \right) \right]$

A) $- 3 w ^ { 2 } - 9 w$
B) $7 w ^ { 2 } - 9 w$
C) $- 3 w ^ { 2 } - 13 w$
D) $7 w ^ { 2 } - 13 w$

Question 76

Simplify.

- $\left( - \frac { 10 } { 11 } x ^ { 2 } y + \frac { 2 } { 3 } \right) - \left( - \frac { 2 } { 11 } x ^ { 2 } y - \frac { 1 } { 6 } \right)$

A) $\frac { 8 } { 11 } x ^ { 2 } y + \frac { 5 } { 6 }$
B) $- \frac { 8 } { 11 } x ^ { 2 } y + \frac { 5 } { 6 }$
C) $\frac { 8 } { 11 } x ^ { 2 } y + \frac { 1 } { 2 }$
D) $- \frac { 8 } { 11 } x ^ { 2 } y + \frac { 1 } { 2 }$

Question 77

Simplify.

- $\left( - \frac { 1 } { 3 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 2 } { 5 } \right) + \left( - \frac { 1 } { 4 } x ^ { 2 } + \frac { 4 } { 5 } x + \frac { 1 } { 2 } \right)$

A) $\frac { 5 } { 6 } x ^ { 2 } + 6 x - 2$
B) $\frac { 29 } { 30 } x ^ { 6 } + \frac { 1 } { 10 }$
C) $- \frac { 7 } { 12 } x ^ { 4 } + \frac { 31 } { 20 } x ^ { 2 } + \frac { 1 } { 10 }$
D) $- \frac { 7 } { 12 } x ^ { 2 } + \frac { 31 } { 20 } x + \frac { 1 } { 10 }$

Question 78

Multiply.

- $( - 5 x y ) \left( - 2 x y ^ { 2 } \right)$

A) $- 10 x y ^ { 3 }$
B) $10 x ^ { 2 } y ^ { 3 }$
C) $- 7 x ^ { 2 } y ^ { 3 }$
D) $10 x y ^ { 2 }$

Question 79

Simplify.

- $\left( 10 a ^ { 2 } b - 12 a b + 8 \right) - \left( 2 a ^ { 2 } b + 2 a b - 4 \right)$

A) $8 a ^ { 2 } b - 14 a b + 12$
B) $12 a ^ { 2 } b - 14 a b + 12$
C) $8 a ^ { 2 } b + 14 a b - 12$
D) $8 a ^ { 2 } b + 14 a b + 12$

Question 80

Simplify.

- $( 14 y + 2 ) - \left[ - 6 y ^ { 2 } - ( 7 y - 2 ) \right]$

A) $6 y ^ { 2 } + 7 y$
B) $6 y ^ { 2 } + 21 y - 4$
C) $- 6 y ^ { 2 } + 7 y + 4$
D) $6 y ^ { 2 } + 21 y$