Math 209 Individual Textbook Solutions Week 1

Individual Assignment Week 1 MTH 209

Due Monday, Week 1 22 problems; 6 points full credit

Show all relevant steps unless instructed otherwise. Simplify and reduce to lowest terms unless otherwise instructed. Exponents & Polynomials (Chapter 4 of Dugo 3rd Ed)

Individual (22 problems) Section 4.1: Page 263, Exercises 50, 66, and 76 Section 4.2: Page 273-275, Exercises 40, 58, 68, 72, 84 Section 4.3: Pages 282-283, Exercises 48, 64 Section 4.4: Pages 288-289, Exercises 34, 68, 78 Section 4.5: Pages 293-295, Exercises 26, 40, and 52 Section 4.6: Page 300, Exercises 46, 74 Section 4.7: Pages 307-308, Exercises 12, 24, 38, and 66

/50 Simplify. All variables represent nonzero real numbers.

− 5y 4 (y 5 ) 2 15y7 (y2)3

Ans: -y/3

/66 Simplify. All variables represent nonzero real numbers.

( 3 y 8 ) 4 ( 2zy2 )4 Ans: (81 y^24) / (16 z^4)

/76 Simplify. All variables represent nonzero real numbers. No steps required for this one. a9 * a0

Ans: a^9

1 Page 274/40 Simplify. See Example 3.

w −4 w6 Ans: 1/ w^10

/58 Simplify. See Example 4.

(2s −1 t 3 ) −3 (6s2 t−4 ) −3 Ans: (27 s^9)/ t^21

/68 Write the number in standard notation. See Example 4.

9.3 X 10 −5

Ans:0.000093

/72 Write the number in standard notation. See Example 4.

8X106 Ans:8000000

/84 Perform the computations. Write answers in scientific notation.

9 X 10 −4 3 X 10 −6

Ans: 3 X 10^2

/48 Perform the operation. See Example 5.

(w2 −2w +1) + (2w − 5 +w2)

Ans: 2 w^2 – 4 OR 2(w^2 - 2)

2 Perform the operation. See Example 6.

(4 −5y + y3) − (2 −3y + y2)

Ans: y^3 – y^2 - 2y +2

/34 Find the product. See Example 2.

(3c2d − d3 +1) 8cd2

Ans: 24 c^3 d^3 - 8 c d^5 + 8 c d^2

/68 Perform the operation.

(5x −6)(5x −6)

Ans: 25x^2 – 60x + 36

/78 Swimming space. The length of a rectangular swimming pool is 2x−1 meters, and the width is x+2 meters. Write a polynomial A(x) that represents the area of the triangle. Find A(5).

Ans : A(x) = ( 2 x^2 +3x -2) sq .m A (5) = 63 sq.m

/26 Use FOIL to find the product. See Example 1. Show FOIL.

(2x − 5y)(x+y) Ans: 2 x^2 – 3xy – 5 y^2

/40 Use FOIL to find the product. See Example 2. Show FOIL.

(5y3 w2 + z)(2y3 w2 +3z) Ans: 10 y^6 w^4 + 17 y^3 w^2 z + 3 z^2

/52 Find the product. Try to write only the answer. See Example 3.

(3h − 5)(3h + 5)

3 Ans: 9 h^2 - 25 Page 300/46 Find the product. See Example 3.

(4u − 9v)(4u +9v) Ans: 16 u^2 – 81 v^2

/74 Find the product.

(3z4 − 8)2 Ans: 9 z^8 – 48 z^4 + 64 Page 307/12 Find the quotient. See Example 1.

b 19 b12 Ans: b^7 Page 307/24 Find the quotient. See Example 1.

− 12 z 10 y 2 −2 z4 y2 Ans: 6 z^6

/38 Find the quotient and remainder (show steps of long division as shown in the Q&A example). Check by using the fact that dividend = (quotient)(divisor) + remainder. See Example 4.

(x2 + 3x + 6) ÷ (x+3) Ans: Quotient is x and the remainder is 6 Dividend = (quotient)(divisor) + remainder x^2 + 3x + 6 = (x)(x+3) + 6 = x^2 + 3x +6 Page 308/66 Use long division (show steps as shown in the Q&A example) and write the expression in the form Quotient + remainder Divisor 2x 2 + 4 2x Ans: Quotient is x and remainder is 4

2x 2x^2 + 4 x 2x^2

4 remainder 4 Ans can be put as x + 4/(2x)