# 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**

**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 **

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.__Perimeter of a rectangle.__

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**

__Perimeter of a rectangle.__

(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**** **

**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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