Reference no: EM13912054
For each polynomial in Problems 1-4, (a) give the degree of the polynomial, (b) give the coefficient (numerical) of the highest-degree term, (c) give the constant term, and (d) decide whether it is a polynomial of one or several variables.
1. 10- 3x- x2 2. 5x4 - 2x9 + 7
3. 7x2y - 14xy3z 4. 2x5 + 7x2y3 - 5y6
The expressions in Problems 5 and 6 are polynomials with the form anxn + an-1xn-1 + ......... + a1x + a0, where n is a positive integer. Complete the following.
5. For 2x5 - 3x2 - 5,
(a) 2 = a? (b) a3 =? ?
(c) -3 = a? (d) a0 = ?
6. For 5x3 - 4x - 17,
(a) a3 = ? (b) a1 = ?
(c) a2 = ? (d) -17 = a?
In Problems 7-12, evaluate each algebraic expression at the indicated values of the variables.
7. 4x - x2 at x = -2
8. 10 - 6(4 - x)2 at x = -1
9. 10xy - 4(x - y)2 at x = 5 and y = -2
10. 3x2 - 4y2 - 2xy at x = 3 and y = -4
11. 2x - y/x2 - 2y at x = -5 and y = -3
12. 16y/1-y at y = -3
13. Evaluate 1.98T - 1.09(1 - H)(T - 58) - 56.8 when T = 74.7 and H = 0.80
14. Evaluate R [0.083i/1- (1 + 0.083i)-n] when R = 100,000, i = 0.07, n = 360.
In Problems 15-22, simplify by combining like terms.
15. (16pq - 7p2) + (5pq + 5p2)
16. (3x3 + 4x2y2) + (3x2y2 - 7x3)
17. (4m2 - 3n2 + 5) - (3m2 + 4n2 + 8)
18. (4rs - 2r2s 2 - 11rs2) - (11rs2 - 2rs + 4r2s)
19. -[8 - 4(q + 5) + q]
20. x3 + [3x - (x3 - 3x)]
21. x2 - [x - (x2 - 1) + 1 - (1 - x2)] + x
22. y3 - [y2 - (y3 + y2)] - [y3 + (1 - y2)]
In Problems 23-60, perform the indicated operations and simplify.
23. (5x3)(7x2)
24. (-3x2y)(2xy3)(4x2y2)
25. (39r3s2) / (13r2s)
26. (-15m3n) / (5mn4)
27. ax2(2x2 + ax + ab)
28. -3(3 - x2)
29. (3y + 4)(2y - 3)
30. (4x - 1)(x - 3)
31. 6(1 - 2x2)(2 - x2)
32. 2(x3 + 3)(2x3 - 5)
33. (4x + 3)2
34. (2y + 5)2
35. (0.1 - 4x)(0.1 + 4x)
36. (x3y3 - 0.3)2
37. 9(2x + 1)(2x - 1)
38. 3(5y + 2)(5y - 2)
39. (x2 -1/2)2
40. (2/3 + x)(2/3 - x)
41. (0.1x - 2)(x + 0.05)
42. (6.2x + 4.1)(6.2x - 4.1)
43. (x - 2)(x2 + 2x + 4)
44. (a + b)(a2 - ab + b2)
45. (x3 + 5x)(x5 - 2x3 + 5)
46. (x3 - 1)(x7 - 2x4 - 5x2 + 5)
47. (a) (3x - 2)2 - 3x - 2(3x - 2) + 5 (b) (3x - 2)2 - (3x - 2)(3x - 2) + 5
48. (a) (2x - 3)(3x + 2) - (5x - 2)(x - 3) (b) 2x- 3(3x + 2) - 5x- 2(x - 3)
49. (18m2n + 6m3n + 12m4n2) / (6m2n)
50. (16x2 + 4xy2 + 8x) / (4xy)
51. (24x8y4 + 15x5y - 6x7y) / (9x5y2)
52. (27x2y2 - 18xy + 9xy2) / (6xy)
53. (x + 1)3
54. (x - 3)3
55. (2x - 3)3
56. (3x + 4)3
57. (x3 + x - 1) / (x + 2)
58. (x5 + 5x - 7) / (x + 1)
59. (x4 + 3.x3 - x + 1) / (x2 + 1)
60. (.x3 + 5x2 - 6) / (x2 - 2)
In Problems 61-68, perform the indicated operations with expressions involving fractional exponents and radicals, and then simplify.
61. x1/2(x1/2 + 2x3/2)
62. x-2/3(x5/3 - x-1/3)
63. (x1/2 + 1)(x1/2 - 2)
64. (x1/3 - x1/2)(4X2/3 - 3x3/2)
65. (√x + 3)(√x - 3)
66. (x1/5 + x1/2)(x1/5 - x1/2)
67. (2x + 1)1/2[(2x + 1)3/2 - (2x + 1)-1/2]
68. (4x - 3)-5/3[(4x - 3)8/3 + 3(4x - 3)5/3]
69. Revenue A company sells its product for $55 per unit. Write an expression for the amount of money received (revenue) from the sale of x units of the product.
70. Profit Suppose a company's revenue R (in dollars) from the sale of x units of its product is given by
R = 215x
Suppose further that the total costs C (in dollars) of producing those x units is given by
C = 65x + 15,000
(a) If profit is revenue minus cost, find an expression for the profit from the production and sale of x units.
(b) Find the profit received if 1000 units are sold.
71. Rental A rental truck costs $49.95 for a day plus 49¢ per mile.
(a) If x is the number of miles driven, write an expres- sion for the total cost of renting the truck for a day.
(b) Find the total cost of the rental if it was driven 132 miles.
72. Cell phones Cell Pro makes cell phones and has weekly costs of $1500 for rent, utilities, and equipment plus labor and material costs of $18.50 for each phone it makes.
If x represents the number of phones produced and sold, write an expression for Cell Pro's weekly total cost.