# Polynomials, Equations, and Radicals

43. (3y+2) (2y^2-y+3)

*44. (4y+ 3) (y^2+3y+1)

46. (m^3-4mn^2)(6m^4n^2-3m^6+m^2n^4)

*90. (5-6y)(3y^2-y-7)

*91. Office Space. The length of a professor's office is x feet, and the width is x+4 feet. Write a polynomial that represents the area. Find the area if x=10ft.

100. If a manufacturer charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts per week. What polynomial represents the total revenue expected for a week? How many shirts will be sold if the manufacturer charges $20 each for the shirts? Find the total revenue when the shirts are sold for $20 each. Use the bar graph to determine the price that will give the maximum total revenue.

68. (x-6)(9x+4)(9x-4)

69. (x-1)(x+2)-(x+3)(x-4)

14. (x+z)^2

16. (3t+v)^2

*21. (t-1)^2

*35. (3x-8)(3x+8)

41. (5x^2-2)(5x^2+2)

*42. (3y^2+1)(3y^2-1)

*81. Shrinking garden. Rose's garden is a square with sides of length x feet. Next spring she plans to make it rectangular by lengthening one side 5 feet and shortening the other side by 5 feet. What polynomial represents the new area? By how much will the area of the new garden differ from that of the old garden?

84. Comparing dartboards. A toy store sells two sizes of circular dartboards. The larger of the two has a radius that is 3inches greater than that of the other. The radius of the smaller dartboard is t inches. Find a polynomial that represents the difference in area between the two dartboards.

30. 6y^6-9y^4+12y^2 / 3y^2

32. -9ab^2-6a^3b^3 / -3ab^2

33. (x^2y^3-3x^3y^2) / (x^2y)

34. (4h^5k-6h^2k^2) / (-2h^2k)

47. (x^3-x^2+x-2) / (x-1)

48. (a^3-3a^2+4a-4) / (a-2)

16. 3xy^8 * 5xy^9 / 20x^3y^14

41. (-6x^2y^4z^9 / 3x^6y^4z^3) ^2

42. (-10rs^9t^4 / 2rs^2t^7) ^3

76. CD rollover. Ronnie invested P dollars in a 2 year CD with a an annual rate of return of r. After the CD rolled over two times, its value was P((1+r)^2)^3. Which law of exponents can be used to simplify the expression? Simplify it.

Answers without negative exponents.

25. -2x^2 * 8x^-6

26. 5y^5(-6y^-7)

Answers in scientific notation.

71. (3x10^5)(2x10^-15)

72. (2x10^-9)(4x10^23)

Answers in scientific notation, round to three decimal places.

94. (8.79x10^8) + (6.48 x10^9)

95. (3.5x10^5)(4.3x10^-6) / 3.4x10^-8

*96. (3.5x10^-8)(4.4x10^-4) / 2.433x10^45

*98. (8x10^99) + (3x10^99)

*105. Extracting metals from ore. Thomas Sherwood studied the relationship between the concentration of a metal in commercial ore and the price of the metal. The accompanying graph shows the Sherwood plot with the locations of several metals marked. Even though the scales on this graph are not typical, the graph can be read in the same manner as other graphs. Note also that a concentration of 100 is 100%.

a) Use the figure to estimate the price of copper (Cu) and its concentration in commercial ore.

b) Use the figure to estimate the price of a metal that has a concentration of 10^-6 percent in commercials ore.

c) Would the four points shown in the graph lie along a straight line if they were plotted in our usual coordinate system?

106. Recycling metals. The accompanying graph shows the prices of various metals that are being recycled and the minimum concentration in waste required for recycling. The straight line is the line from the figure for Exercise 105. Points above the line correspond to metals for which it is economically feasible to increase recycling efforts.

a) Use the figure to estimate the price of mercury (Hg) and the minimum concentration in waste required for recycling mercury.

b) Use the figure to estimate the price of Silver (Ag) and the minimum concentration in waste required for recycling silver.

Use the product rule to simplify each expression.

Simplify each radical.

Write each radical expression in simplified radical form.

#### Solution Summary

Answers to questions on Polynomials, Equations, and Radicals etc.