Algebra 1 Quarter 3 Exam (Unit 8 & Review from Previous Units)mrsbrantleymath.weebly.com/uploads/5/6/2/9/56291093/... · 2020. 3. 5. · Name: Date: _____ Algebra 1 – Quarter 3

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

1. The graph of f (x) is shown. Which statement about f (x) is true?

a. The zero of f (x) is -2.

b. The zero of f (x) is 2.

c. The zeros of f (x) are −2 and -4.

d. There are no zeros.

2. Find the zeros of the function.

3. Solve 𝑥2 + 3𝑥 − 4 = 0 using a graphing calculator.

a. 𝑥 = −4, 𝑥 = −1

b. 𝑥 = 4, 𝑥 = −1

c. 𝑥 = 4, 𝑥 = 1

d. 𝑥 = −4, 𝑥 = 1

4. Solve 𝑥2 − 4x − 5 = 0 using a graphing calculator.

5. Which quadratic equation has zeroes of 6 and 2?

a. 𝑦 = 𝑥2 + 8𝑥 − 12

b. 𝑦 = 𝑥2 − 8𝑥 − 12

c. 𝑦 = 𝑥2 − 8𝑥 + 12

d. 𝑦 = 𝑥2 + 8𝑥 − 12

6. Which quadratic equation has the solutions -1 and -3?

a. 𝑦 = 2𝑥2 − 𝑥 − 3

b. 𝑦 = 4𝑥2 + 7𝑥 + 3

c. 𝑦 = 𝑥2 − 4𝑥 + 3

d. 𝑦 = 𝑥2 + 4𝑥 + 3

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

7. Use your graphing calculator to identify the vertex and the y-intercept of the graph of the function

𝑓(𝑥) = 3(𝑥 − 2)2 + 5

a. vertex:(2, 5);

y-intercept: 17

b. vertex: (−2, −5);

y-intercept: 12

c. vertex:(2, −5);

y-intercept: 12

d. vertex:(−2, 5);

y-intercept: 17

8. Use your graphing calculator to identify the vertex and the y-intercept of the graph of the function

𝑓(𝑥) = 2(𝑥 + 3)2 − 6

a. vertex:(3,6);

y-intercept: 6

b. vertex: (−3, −6);

y-intercept: 12

c. vertex:(3,6);

y-intercept: 12

d. vertex:(−3, −6);

y-intercept: 6

9. Write an equation for the parabola whose vertex is at (−4, −7) and which passes through (−9, −57).

a. 𝑦 = 2(𝑥 + 4)2 + 7

b. 𝑦 = (𝑥 + 4)2 − 7

c. 𝑦 = 2(𝑥 − 4)2 + 7

d. 𝑦 = −2(𝑥 + 4)2 − 7

10. Write an equation for the parabola whose vertex is at (−4, 2) and which passes through (−7, −34).

a. 𝑦 = 4(𝑥 + 4)2 + 2

b. 𝑦 = −4(𝑥 + 4)2 + 2

c. 𝑦 = −4(𝑥 − 4)2 + 2

d. 𝑦 = −4(𝑥 − 4)2 − 2

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

11. The height of a ball after its been thrown can be modeled by the expression: ℎ = −𝑥2 − 4𝑥 + 21.

Which statement about the height of the ball is true?

a. The expression −(x +2)2

+ 25 reveals a maximum height of 2 feet.

b. The expression −(x +2)2

+ 25 reveals a maximum height of 25 feet.

c. The expression −(x +2)2

− 25 reveals a maximum height of 2 feet.

d. The expression −(x +2)2

− 25 reveals a maximum height of 25 feet.

12. The spray of a fountain has a height, in feet that can be modeled by the polynomial expression

𝑦 = −𝑥2 + 12𝑥 − 32. Which statement about the height of the spray is true?

a. The expression −(𝑥 − 6)2 + 4 reveals a maximum height of 6 feet.

b. The expression −(𝑥 − 6)2 + 4 reveals a maximum height of 4 feet.

c. The expression −(𝑥 + 6)2 + 4 reveals a maximum height of 6 feet.

d. The expression −(𝑥 + 6)2 + 4 reveals a maximum height of 4 feet.

13. The function 𝑓(𝑥) = −16𝑡2 + 128 models the height 𝑓(𝑥) in feet of a stone t seconds after it is

dropped from the edge of a vertical cliff. Approximately how long will it take the stone to hit the

ground?

a. 6.95 seconds

b. 0.36 seconds

c. 3.14 seconds

d. 2.83 seconds

14. Water that is sprayed upwards from a sprinkler with an initial velocity of 20 m/s can be approximated by

the function 𝑦 = −5𝑥2 + 20𝑥, where y is the height of a drop of water x seconds after it is released.

Find the time it takes the water to reach the ground.

a. 1 second

b. 2 seconds

c. 3 seconds

d. 4 seconds

15. A rocket was launched straight up with an initial velocity of 128 feet per second. The function

ℎ(𝑡) = −16𝑡2 + 128𝑡 represents the height of the rocket, in feet, t seconds after it was launched.

How many seconds did the rocket take to return to the ground?

a. 2

b. 4

c. 6

d. 8

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

16. Identify the vertex and the axis of symmetry of the

parabola.

a. Axis of Symmetry: 𝑥 = 7

Vertex: (7, −2)

b. Axis of Symmetry 𝑥 = −2

Vertex: (−2, 7)

c. Axis of Symmetry x = -7

Vertex : (-7, -2)

d. Axis of Symmetry x = 2

Vertex: (2, -7)

17. Identify the vertex and the axis of symmetry of the parabola.

Vertex:

Axis of Symmetry:

18. Use the quadratic formula to solve the equation 6𝑥2 + 7𝑥 − 49 = 0. Round your answer to the

hundredths place.

a. 𝑥 = −1.45, 𝑥 = −2.87

b. 𝑥 = 3.5, 𝑥 = −2.33

c. 𝑥 = −3.5, 𝑥 = 2.33

d. 𝑥 = 2.87, 𝑥 = −3.4

19. Use the quadratic formula to solve the equation 2𝑥2 − 9𝑥 − 5 = 0.

a. 𝑥 = −5 and 𝑥 = −1

b. 𝑥 = −1

2 and 𝑥 = 5

c. 𝑥 =1

2 and 𝑥 = −5

d. 𝑥 = 5 and 𝑥 = 1

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

20. Solve by factoring 2𝑥2 + 9𝑥 + 4 = 0

a. 𝑥 = −1

2, 𝑥 = −4

b. 𝑥 = 4, 𝑥 = 1

2

c. 𝑥 = 4, 𝑥 = 2

d. 𝑥 = −4, 𝑥 = −2

21. Solve by factoring 2𝑥2 − 2𝑥 − 4 = 0

a. 𝑥 = 2 and 𝑥 = 1

b. 𝑥 = −2 and 𝑥 = −1

c. 𝑥 = 2 and 𝑥 = −1

d. 𝑥 = −2 and 𝑥 = 1

22. Jim has his own farm. He wants to make more money on his crop yield next spring, so

he is increasing the area where he plants. He is increasing the length of the rectangular

area by 5 feet and the length by 8 feet. The width and height must increase by the same

amount of feet, x. Which equation represents all the possible areas for his new farm?

a. A = x2

+ 13x + 40, where x is any real number

b. A = x2

+ 13x + 40, where x is any nonnegative real number

c. A = 2x + 13, where x is any real number

d. A = 2x + 13, where x is any nonnegative real number

23. James loves to farm and loves to make money. He wants to make the maximum amount

of money on his potato farm for next spring, so he decided that he wants to increase the

area where he plants the potatoes. He is increasing the length of the rectangular area by

15 feet and the length by 8 feet. The width and height must increase by the same

amount of feet, x. What equation would represent the possible area for James new

potato farm?

a. A = x2

+ 23x + 120, where x is any nonnegative real number

b. A = x2

+ 23x + 120, where x is any real number

c. A = 2x + 120, where x is any real number

d. A = 2x + 120, where x is any nonnegative real number

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

24. The graph of 𝑦 = 𝑥2 is translated 4 units to the right and 2 units down. What is the

equation of the transformed function?

a. (𝑥 − 2)2 − 4

b. (𝑥 + 2)2 + 4

c. (𝑥 + 4)2 − 2

d. (𝑥 − 4)2 − 2

25. The graph of 𝑦 = 𝑥2 is translated 3 units to the left and 5 units up. What it the equation

of the transformed function?

a. (𝑥 + 3)2 + 5

b. (𝑥 − 3)2 − 5

c. (𝑥 + 3)2 − 5

d. (𝑥 − 3)2 + 5

26. A construction company determines that the number of wooden beams it can sell is given by

the formula 𝐷 = −3p2 + 180p − 285, where p is the price of the beams in dollars. Using

this information answer the following two questions. 1.) At what price will the

construction company sell the maximum number of wooden beams and 2.) What is the

maximum number of wooden beams that can be sold?

a. $26; 2367 drills

b. $30; 2415 drills

c. $35; 2305 drills

d. $20 2110 drills

27. A small independent motion picture company determines the profit P for producing n DVD

copies of a recent release in 𝑃 = −0.02𝑛2 + 3.40𝑛 − 16. P is the profit in thousands of dollars

and n is in thousands of units. 1.) How many DVDs should the company produce to maximize

the profit? 2.) What will the maximum profit be?

a. 65 DVD’s, $120.50

b. 90 DVD’s, $130.00

c. 75 DVD’s, $126.50

d. 85 DVD’s, 128.50

28. A pharmacist t is using the function 𝑃(𝑡) = 𝑡2 + 𝑡 + 1 to calculate the number of

prescriptions filled after t minutes. How many minutes (t) have passed when there are

133 prescriptions filled (P) present in the pharmacy?

a. 9

b. 10

c. 14

d. 11

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

29. A chemist t is using the function 𝑃(𝑡) = 𝑡2 + 2𝑡 + 1 to calculate the number of

prescriptions filled after t minutes. How many minutes (t) have passed when there are

256 prescriptions filled (P) present in the pharmacy?

a. 8

b. 10

c. 12

d. 15

30. A tennis ball A tennis ball is hit upward at a velocity of 7 meters per second from a height that is 12

meters above the ground. The height h (in meters) of the ball at time t seconds after it is thrown can be

found by the formula: ℎ = −3𝑡2 + 12𝑡 + 15. Find the time (t) when the ball is again 15 meters (h)

above the ground.

a. 3 seconds

b. 5 seconds

c. 2 seconds

d. 4 seconds

31. A fireworks shell is fired from a mortar. Its height is modeled by the function

ℎ(𝑡) = −16(𝑡 − 7)2 + 784, where t is the time in seconds and h is the height in feet. Find the time (t)

when the firework will be 720 feet from the ground. If the firework reaches 720 feet above the ground at

two different times include both.

a. The firework never reaches 720 feet

b. 5 seconds

c. 9 seconds

d. 5 seconds & 9 seconds

32. Use the graph of 𝑦 = 𝑥2 − 3 to answer the following question. If you translate the parabola to the left 3

units and up 5 units, what is the equation of the new parabola in vertex form?

a. (𝑥 + 3)2 + 2

b. (𝑥 − 3)2 + 2

c. (𝑥 + 3)2 + 5

d. (𝑥 − 3)2 − 5

33. Use the graph of 𝑦 = 𝑥2 + 2 to answer the following question. If you translate the parabola to the right

3 units and down 7 units, what is the equation of the new parabola in vertex form?

a. (𝑥 + 3)2 − 7

b. (𝑥 − 3)2 − 7

c. (𝑥 + 3)2 + 5

d. (𝑥 − 3)2 − 5

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

34. Marcus is bungee jumping for the first time off a local bridge. As

instructed, he leaps up off the ledge and jumps outwards. His movement

can be modeled as 𝑦 = −2𝑥2 + 20𝑥 + 151, where x is measured in feet.

What is a reasonable range for the function?

a. All real numbers

b. 0 ≤ 𝑥 ≤ 200

c. −5 ≤ 𝑦 ≤ 15

d. 𝑦 ≥ −5

35. An architect proposes a design that uses

𝑦 = −0.08𝑥2 + 2.88𝑥 to model the height of the ceiling in feet

at a distance x feet from the bottom left. What is the range for

the function?

a. All real numbers

b. 𝑦 ≤ 18

c. 0 ≤ 𝑦 ≤ 25.92

d. 18 ≤ 𝑦 ≤ 25.92

Name: Date: _______

Algebra 1 – Quarter 3 Exam (Unit 8 & Review from Previous Units)

36. A polynomial function contains the factors x, x − 5, and x + 2. Which graphs could represent the

polynomial function? Select two that apply.

37. Which quadratic function in vertex form represents 2𝑥2 + 12𝑥 + 4.

a. 𝑦 = 2(𝑥 + 12)2 + 14

b. 𝑦 = 6(𝑥 + 9)2 − 4

c. 𝑦 = (𝑥 + 3)2 + 14

d. 𝑦 = 2(𝑥 + 3)2 − 14

38. Rewrite the quadratic function 𝑦 = 𝑥2 − 8𝑥 − 17 into vertex from.

a. 𝑦 = (𝑥 + 4)2 − 33

b. 𝑦 = (𝑥 − 4)2 − 33

c. 𝑦 = (𝑥 − 1)2 − 24

d. 𝑦 = (𝑥 − 5)2 − 32

a. b. c.

d. e.

f.

39. Ms. Salgado needs to have her car repaired but does not want to spend more than $375 for the repairs. The

mechanic says that the part needed for the repair will cost $100 and the labor will cost an additional $40 per

hour. Which inequality below represents the greatest number of hours the mechanic can work without

exceeding Ms. Salgado’s budget?

a. 140𝑥 ≤ 375

b. 40 + 100𝑥 > 225

c. 100 + 40𝑥 ≤ 375

d. 100 + 40𝑥 > 375

40. Jason is saving up to buy a digital camera. He needs at least $490 to buy the camera. So far, he saved $175. He plans

to save money each week for three weeks. Which equation below can be used to represent how much he must save

every week to have enough money to purchase the camera?

a. 175 + 3𝑥 ≥ 490

b. 175𝑥 + 3 ≥ 490

c. 175 + 3𝑥 ≤ 490

d. 175𝑥 + 3 ≤ 490

41. Ms. Lacy wants to work out. Drop It Like It’s Hot gym charges a monthly rate of $25 and a $5.00 for each class.

Kickin’ It gym charges $20.00 monthly and $7.50 per class. How many classes would Ms. Lacy need to attend for

Kickin’ It gym to be less expensive than Drop It Like It’s Hot gym?

a. More than 2 classes c. Less than 12 classes

b. Less than 2 classes d. More than 12 classes

42. Ms. Hillegass and Ms. Lacy are going on a trip. Ms. Hillegass has $100 and will save $35 each week. Ms. Lacy has

$75.00 and will save $40.00 each week. In how many weeks will Ms. Hillegass have save the amount as Ms. Lacy?

a. 5 weeks

b. 10 weeks

c. 12 weeks

d. 15 weeks

43. Solve the equation: 2𝑥 − 2 = 13𝑥 − 33

a. 31

11

b. −31

11

c. 11

31

d. −11

31

44. Solve the equation: 2𝑥 − 114 = −54

a. 𝑥 = 10

b. 𝑥 = 20

c. 𝑥 = 25

d. 𝑥 = 30

45. What is the domain of the relation below?

a. 0 ≤ 𝑥 ≤ 6

b. 0 ≤ 𝑥 ≤ 10

c. −6 ≤ 𝑥 ≤ 6

d. −6 ≤ 𝑥 ≤ 10

46. What is the domain of the relation below?

a. All real numbers

b. 𝑦 ≤ 2

c. 𝑥 ≤ 2

d. 𝑥 ≥ −3

47. Alex rents a car for one day. The charge is $18 plus $0.25 per mile. How much would Alex be charged if she drives

from Nashville, TN to Panama City Beach, Florida (456 miles)?

a. $8,208.25

b. $132.00

c. $1806.00

d. $96.00

48. An appliance repair shop charges a $60 service fee plus $35 per hour for labor. The equation that models this situation

is 𝑐(ℎ) = 35ℎ + 60 where h is the number of hours of labor and 𝑐(ℎ) is the total cost. How much would the customer

pay for a job that takes 12.5 hours?

a. $450.50

b. $380.75

c. $620.00

d. $497/50

49. Your home state uses a linear model 𝑦 = 22(𝑥 − 70) + 4338 to predict the number of vacationers (y) as compared to

the average temperature of the week (x). Find the number of vacationers predicted for a week with an average

temperature of 68 degrees.

a. 7374 vacationers

b. 5764 vacationers

c. 95,392 vacationers

d. 4294 vacationers

50. Select 3 ordered pairs that are found on the function 𝑓(𝑥) = −3(𝑥 + 2)2 − 𝑥

a. (-5, 22)

b. (-28, 1)

c. (-8, -4)

d. (-3, 0)

e. (-2, 2)

51. Select 2 ordered pairs that are found on the function 𝑓(𝑥) = −1

4(𝑥 − 1)2 − 3𝑥

a. (0, 0)

b. (11, -58)

c. (1, -3)

d. (-14, -30)

52. A climber is in on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.

What is the average rate of change?

a. 200 feet/hour

b. 150 feet/hour

c. 75 feet/hour

d. 300 feet/hour

53. Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400.

What is the rate of change of money in his savings account per week?

a. $50/week

b. 50 weeks/dollars

c. $10/week

d. 10 weeks/dollars

54. The table below shows the number of CD players sold in a small electronics store

in the years 1989 – 1999. What was the average rate of change of sales between

1989 and 1999?

a. 640 CD players/year

b. 64 CD players/year

c. 100 CD players/year

d. 10 CD players/year

e. 25 CD players/year

55. What is the rate of change for this table? Use correct units in your answer.

Hours Money

0 $0

1 $9

2 $18

3 $27

4 $36

56. Which is NOT a linear function?

a. 𝑦 = 8𝑥

b. 𝑦 = 𝑥 + 8

c. 𝑦 =8

𝑥

d. 𝑦 = 8 − 𝑥

57. What TWO graphs represent a linear function?

58. The cost to attend the Nashville Zoo is $5 per person

with a maximum of $30 for a family of 6 or more. This

situation can be represented by the following step

function and graph:

{5𝑥 𝑖𝑓 0 ≤ 𝑥 < 630 𝑖𝑓 𝑥 ≥ 6

}

Jane wants to go to the zoo this Saturday. She plans to go

with her mom, her dad and her two little brothers. How

much will it cost for her family of 5 to go to the zoo?

a. $15

b. $20

c. $25

d. $30

59. An ice skating arena charges an admission fee for each child plus a rental fee for each pair of ice skates. John paid the

admission fees for his six nephews and rented five pairs of ice skates. He was charged $32.00. Juanita paid the

admission fees for her seven grandchildren and rented five pairs of ice skates. She was charged $35.25. What is the

cost of the rental ice skates?

a. $32.00 b. $35.25 c. $2.50 d. $6.50

60. At a Columbia Central High School basketball game, Noeli bought five hot dogs and three sodas for $17. At the same

time, Anna bought two hot dogs and four sodas for $11.00. Find the cost of one hot dog and one soda.

a. Hot dogs = $3.00; soda = $1.00

b. Hot dogs = $3.25; soda = $1.75

c. Hot dogs = $1.50; soda = $1.50

d. Hot dogs = $2.50; soda = $1.50

61. Tom has a collection of 30 CDs and Nita has a collection of 12 CDs. Tom is adding 2 CDs a month to his collection

while Nita is adding 4 CDs a month to her collection. Select the graph and system to find the number of months after

which they will have the same number of CDs. Let x represent the number of months, and y the number of CDs.

62. What is the solution of the system of equations?

𝑥 + 2𝑦 = −6

3𝑥 + 8𝑦 = −20

a. (-1, -4)

b. (-4, 4)

c. (-4, -1)

d. (3, 1)

63. A system of equations is shown below. What is the first step in the system of equations?

{3𝑥 − 5𝑦 = 11 𝑥 − 3𝑦 = 1

}

a. Add equation one and equation two to cancel out the y’s. b. Subtract equation one and equation two to cancel out the y’s.

c. Divide the first equation by 3 and add the results to the second equation.

d. Multiply the second equation by a -3 and add the results.

64. Mrs. Brantley bought 2 lattes and 4 cinnamon rolls for $18. Ms. Lacy bought 4 lattes and 2 cinnamon rolls for $12.

Find the prices of the lattes and cinnamon rolls.

a. Lattes = $1, Cinnamon Rolls = $4

b. Lattes = $4, Cinnamon Rolls = $1

c. Lattes = $3, Cinnamon Rolls = $4

d. Lattes = $4, Cinnamon Rolls = $3

65. Which of the following solutions is the equation of an increasing exponential function?

a. 𝑦 = (2

3) 𝑥2

b. 𝑦 = (2)𝑥

c. 𝑦 = 8𝑥 + 1

d. 𝑦 = (1

5)

𝑥

66. For the following function, determine if they are increasing or decreasing and by what amount:

a. 𝑦 = 2(1.04)𝑥

b. 𝑦 = 5(1.37)𝑥

c. 𝑦 = −1(0.82)𝑥

d. 𝑦 = 6(1.5)𝑥

e. 𝑦 = −2(0.97)𝑥

f. 𝑦 = 7(1.035)𝑥

67. The data estimated for the state of Tennessee for students enrolled in homeschool between 2017 – 2018 year is

modeled by the function 𝑓(𝑥) = 32,297(1.03)𝑥. Is the student enrollment increasing or decreasing and by what

percent?

a. Decreasing by 0.97%

b. Increasing by 1.03%

c. Increasing by .03%

d. Increasing by 3%

68. Write an equation that models the following situation. Samantha’s hair was known to grow very rapidly. It began at a

length of 6 inches and grew at a rate of 14% a week.

a. 𝑦 = 6(0.14)𝑥

b. 𝑦 = 6(1.14)𝑥

c. 𝑦 = 6(1 + 14)𝑥

d. 𝑦 = 6(0.86)𝑥

69. The value of a car is $15,000. And depreciates at a rate of 8% per year. What is the exponential equation?

a. 𝑦 = 8(15,000)𝑥

b. 𝑦 = 15,000(0.92)𝑥

c. 𝑦 = 15,000(1.08)𝑥

d. 𝑦 = 15,000(0.08)𝑥

70. A coffee is sitting on Mr. Hunt’s desk cooling. It cools according to the function 𝑇 = 70(0.80)𝑥 + 20, where x is the

time in minutes and T is the temperature in degree Celsius. What is the temperature of Mr. Hunt’s coffee after 10

minutes? Round to the nearest tenth.

a. 7.5 degrees

b. 20 degrees

c. 27.5 degrees

d. 76 degrees

71. Suppose a $125,000 piece of machinery is depreciating at 8.5% a year. How much will it be worth after 3 years?

a. $421.88

b. $95,757.61

c. $76.77

d. $159,661.14

72. The area of a rectangular pool is given by the trinomial 3𝑥2 − 2𝑥 − 65. Determine the dimensions of the pool by

factoring.

a. 3𝑥 + 13 and 𝑥 – 5

b. 13𝑥 + 3 and 𝑥 – 5

c. 13𝑥 – 3 and 𝑥 + 5

d. 3𝑥 – 13 and 𝑥 + 5

73. Factor the trinomial completely: 2𝑥2 + 2𝑥 − 4

a. (𝑥 + 4)(𝑥 − 2)

b. (𝑥 + 2)(𝑥 − 1)

c. 2(𝑥 + 1)(𝑥 − 2)

d. 2(𝑥 + 2)(𝑥 − 1)

74. Select 2 expressions that are equivalent to 2𝑥2 − 18 = 0

a. 2(𝑥2 − 9)

b. 2(𝑥 − 9)2

c. 2(𝑥 − 3)2

d. 2(𝑥 − 3)(𝑥 + 3)

75. Factor the trinomial completely: 15𝑥2 − 27𝑥 − 6

a. 3(5𝑥2 − 9𝑥 − 2)

b. (𝑥 − 2)(5𝑥 + 1)

c. 3(𝑥 − 2)(5𝑥 + 1)

d. (𝑥 − 2)(15𝑥 + 3)

76. Find the sum of (5𝑥2 − 2𝑥 + 1) and (𝑥2 − 4𝑥 + 6)

a. 6𝑥4 − 6𝑥2 + 7

b. 6𝑥2 − 6𝑥 + 7

c. 4𝑥2 + 2𝑥 − 5

d. 5𝑥4 + 8𝑥2 + 6

77. If the perimeter of the triangle is 2𝑥2 + 5𝑥 + 6, find the length of the missing side.

a. 𝑥2 + 5𝑥 + 9

b. 𝑥2 + 3𝑥 + 8

c. 2𝑥2 + 𝑥 − 7

d. 2𝑥2 + 5𝑥 + 6

78. If the perimeter of the triangle is represented by 6𝑥 − 9, find the length of the missing side.

a. 𝑥 + 4

b. 3𝑥 − 2

c. 2𝑥 − 7

d. 2𝑥 − 9

2𝑥 − 3 𝑥2 + 1

𝑥 + 4

3𝑥 − 2