1. Is 2x5 – 9x – 6 a polynomial? If not, why not?
no; negative exponent

2. Is – 5x2 – 6x + 8 a polynomial? If not, why not?
yes

3. Give the degree of 3x3y + 4xy and identify the type of polynomial by special name. If no special name applies, write “polynomial.”
4; binomial

4. Give the degree of 6a4b6 and identify the type of polynomial by special name. If no special name applies, write “polynomial.”
10; monomial

5. Evaluate 19 – 3x when x = – 9 and y = 6.46

6. Evaluate – 8x + y2 when x = – 9 and y = 6.
108

7. Evaluate 2x2 + xy + y when x = – 9 and y = 6.
114

8. Add (– 9x2 + 14) + (7x – 2).
– 9x2 + 7x + 12

9. Add (x2 + 5xy – 9) + (x2 – 3xy).
2x2 + 2xy – 9

10. Add (– 6a2 – ab + 6b2) + (a2 + 4ab – 11b2).

11. Add (x2 – y) + (– 7x2 + 9y2 – 8y).
– 6x2 + 9y2 – 9y

12. Add (14x2 – 9x) + (6x2 – 3x + 28).
20x2 – 12x + 28

13. 2 9
1 5
3 8
Add ( m3 + 6m2 – m + ) + ( m2 – m – 6).
3 2
4 5
m m2 – m – 29
15 2
45 8

14. Add (5.8x + 2.4y – 5.7) + (– 8.2y ).
5.8x – 5.8y + 6.7

15. Find the opposite (additive inverse) of – 7x + 8.

16. Find the opposite (additive inverse) of 21x – 9.

17. Find the opposite (additive inverse) of 10a – 6b + 14.

18. Subtract (– 9x – 7) – 15.
– 9x – 22

19. Subtract 6x – (5x + 18).
x – 18

20. Subtract (2y – 12) – y.
y – 12

21. Subtract (– 8x2 – 2x + 9) – (5x2 + 16x – 3).

22. Subtract (– 4a2 + 3a – 8) – (9a2 – 7).

23. Multiply – 7x5(8x10).
– 56x15

24. Multiply 9y(– 16y8).
– 144y9

25. Multiply 3z8(8z2).
24z10

26. Multiply – 3x2(7x2 – x – 17).
– 21x4 + 3x3 + 51x2

27. Multiply 2x4(9x2 – 3x + 5).
18x6 – 6x5 + 10x4

28. Multiply x(– 8x5 + 13x3 + 21).
– 8x6 + 13x4 + 21x

29. Multiply – 5a2(4a4 – 9a2 + 7).
– 20a6 + 45a4 – 35a2

30. Multiply (x + 8)(x – 2).
x2 + 6x – 16

31. Multiply (x – 12)(x – 3).
x2 – 15x + 36

32. Multiply (x + 5)(x – 3).
x2 + 2x – 15

33. Multiply (x – 9)(x – 6).
x2 – 15x + 54

34. Multiply (x – 10)(x + 7).
x2 – 3x – 70

35. Multiply (6x – 3)(9x – 1).
54x2 – 33x + 3

36. Multiply (– 4x + 6)(2x + 7).
– 8x2 – 16x + 42

37. Multiply (8x + 3)(5x – 2).
40x2 – x – 6

38. 12x9y3 4x6y
Divide
3x3y2

39. 15x3y8 5x5y7
Divide
3x – 2y

40. 96a6b3 12a9b2
Divide
8a – 3b

41. 7x5 + 28x4 7x2
Divide
x3 + 4x2

42. 84a8 – 28a 14a5
Divide
6a3 – 2a – 4

43. 4x5 – 16x4 + 36x3 2x3
Divide
2x2 – 8x + 18

44. Divide .
– 200x4y4z2 – 150x2y6z8 + 25xy2z5 5xy4z
– 40x3z – 30xy2z7 + 5y – 2z 4

45. Neil has four more quarters than dimes in his pocket
Neil has four more quarters than dimes in his pocket. If you let d = the number of dimes, how would you represent the number of quarters?
d + 4

46. Jerry’s collection of nickels totals $6. 40
Jerry’s collection of nickels totals $6.40. Write an equation to find the number of nickels he has in his collection. Do not solve.
5x = 640

47. 15 nickels, 21 quarters, and 105 dimes
Abe has six more quarters than nickels and five times as many dimes as quarters. If he has a total of 141 coins, how many of each coin does he have?
15 nickels, 21 quarters, and 105 dimes

48. Charity has 42 more pennies than dimes
Charity has 42 more pennies than dimes. Hope has seven times as many pennies as dimes. Both of them have the same number of dimes, and together they have $5.46.

49. Charity: 60 pennies and 18 dimes; Hope: 126 pennies and 18 dimes
Find the number of dimes and pennies each has.
Charity: 60 pennies and 18 dimes; Hope: 126 pennies and 18 dimes

50. 24 fives, 8 twenties, and 22 fifties
Dustan has $1,380. He has three times as many fives as twenties. He has six more than two times as many fifties as twenties. How many of each bill does he have?
24 fives, 8 twenties, and 22 fifties

51. State the mathematical significance of Acts 27:22.