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MTH209 Week 1 Homework Quiz Solution Key

Exponents & Polynomials (Chapter 4 of Dugo 2nd Ed)

Individual (26 problems)
Section 4.1 Exercises Pages 253-256 Problems 30, 46, 60, 92
Section 4.2 Exercises Pages 260-263 Problems 18, 30, 84, 94
Section 4.3 Exercises Pages 266-267 Problems 26, 40, 96
Section 4.4 Exercises Pages 271-273 Problems 46, 72, 86
Section 4.5 Exercises Pages 280-281 Problems 12, 30, 92, 94
Section 4.6 Exercises Pages 286-287 Problems 26, 42, 58
Section 4.7 Exercises Pages 295-298 Problems 22, 58, 70, 74, 88

 

Page 253-256, # 30, 46, 60, 92

  1. Evaluate for x = 2

               
-2(2)^4 – 3(2)^2 + 5(2) – 9
-2(16) – 3(4) + 10 – 9
-32 – 12 + 10 – 9
-43


46.       Perform the indicated operations

         
w^2 + w^2 – 2w + 2w + 1 – 5
2w^2 - 4

 

60.       Perform the indicated operations

t^2 – 6t + 7 – 5t^2 + 3t + 2
-4t^2 – 3t + 9

  1. Perimeter of a rectangle. The width of a rectangular playground is 2x – 5 feet, and the length is 3x + 9 feet. Write a polynomial P(x) that represents the perimeter and then evaluate this perimeter polynomial if x is 4 feet.

           
P(x) = 2W(x) + 2L(x)
P(x) = (4x – 5) + (6x + 18)
P(4) = (16 – 5) + (24 + 18)
Perimeter = 53 feet

 

Page 260-263, # 18, 30, 84, 94

18.       Find the product

(5) h * h^8 * k^3
5h^9k^3

           

30.       Find the product

          
7x^5 – 35x^4 – 7x^2

 

84.       Perform the indicated operation

25x^2 – 30x – 30x + 36
25x^2 – 60x + 36

           

94.       Swimming space. The length of a rectangular swimming pool is 2x – 1 meters, and the width is x + 2 meters. Write a polynomial that represents the area. Find the area if x is 5 meters.

            (2x – 1)(x + 2)
2x^2 + 4x – x – 2
2x^2 + 3x – 2
2(5)^2 + 3(5) – 2
50 + 15 – 2
Area = 63 Square Meters

           

Page 266-267, # 26, 40, 96

26.       Use FOIL to find the product.

2x^2 + 2xy – 5xy – 5y^2
2x^2  – 3xy – 5y^2

           

40.       Use FOIL to find the product.

10y^6w^4 + 15y^3w^2z + 2y^3w^2z

96.       Area of a parallelogram. Find a trinomial that represents the area of a parallelogram whose base is 3x+2 meters and whose height is 2x+3.

            (3x + 2)(2x + 3)
6x^2 + 9x + 4x + 6
6x^2 + 13x + 6

 

Page 271- 273, # 46, 72, 86

46.       Find the product.

9y^4 – 3y^2 + 3y^2 – 1
9y^4 - 1

72.       Find the product.

(3z^4 – 8) (3z^4 – 8)
9z^16 – 24z^4 – 24z^4 + 64
9z^16 – 48z^4 + 64

86.       Square lot. Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had?

            A = 155 * 159
A = 24,645 square feet
24,649 – 24,645 = 4
Sam has 4 square feet less than he thought he had.


Page 280-281, # 12, 30, 92, 94

12.       Simplify

-1 – 1
-2

30.       Find each quotient. Try to write only the answer.


92.       Find the quotient

 

  1.  Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x+6 yards. If the width is x yards, find a binomial that represents the length.

            (6x + 6)(x)
6x^2 + 6x

Page 286-287, # 26, 42, 58

26.       Simplify


2y^-2 y^-2
2y^-4

42.       Simplify

 

58.       Simplify each expression. Your answer should be an integer or a fraction. Do not use a calculator.

           

Page 295-298, # 22, 58, 70, 74, 88, 116

22.       Simplify

           

58.       Simplify. Write the expression without negative exponents.

 

(p -5) -9 (p -6)4
(p -8)0 (p 4) -5

 

           

70.       Write the number in standard notation.
9.3 X 10 ^-5
0.000093

  1. Write the number in standard notation.

        8 X 10^6
      8,000,000

 88.      Perform the computations. Write answers in scientific notation.


2.5 x 10^-16

 

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