# MTH209 Week 2 Homework Quiz Solution Key

**Week 2 – Factoring (Chapter 5 of Dugo 2nd Ed)**

Section 5.1 Exercises Pages 316-318 Problems 38, 66, 92, 94

Section 5.2 Exercises Pages 323-325 Problems 14, 60, 78

Section 5.3 Exercises Pages 330-332 Problems 56, 64, 104, 108

Section 5.4 Exercises Pages 338-340 Problems 40, 66, 102

Section 5.5 Exercises Pages 344-346 Problems 32, 66, 106

Section 5.6 Exercises Pages 353-356 Problems 18, 32, 44, 60, 96

Page 317 /38

**Find the Greatest Common Factor (GCF) for the group of monomials.**

**16x2 z, 40 x z2, 72 z3**

16x^2z = 8*2*x*x*z

40xz^2 = 8*5*x*z*z

72z^3 = 8*9*z*z*z

**GCF = 8z**** **

Page 317 /66

**Factor out the GCF.**

**15x2 y2 − 9xy2 + 6x2y**

**3xy(5xy-3y+2x)**** **

Page 317 /92

__Area of Painting.__ A rectangular painting with a width of x centimeters has an area of x2 + 50x square centimeters. Find a binomial that represents the length. See the picture on page 318.

x^2 + 50x = area in square feet

**Length = x + 50**** **

.

Page 318 /94.

__Amount of an investment.__ The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + P*r*t

**a) Rewrite this formula by factoring out the greatest common factor (GCF) on the right-hand side.**

**A = P(1 + rt)**** **

**b) Find A if $8300 is invested for 3 years at a simple interest rate of 15%.**

A = 8,300 + (8,300*3*.15)

A = 8,300 + 3,735

**A = 12,035**** **

Page 323 /14

**Factor the polynomial completely.**

**9a2 − 64b2**

(3a)^2 – (8b)^2

**(3a + 8b)(3a – 8b)**

Page 324 /60

**Factor the polynomial completely.**

**x3 y + 2 x2 y2 + xy3**

xy(x^2 + 2xy + y^2)

**xy(x + y)(x + y)**** **

Page 324 /78

**Use grouping to factor each polynomial completely (You must show grouping).**

**x3 + ax + 3a + 3x2**

(x^3 + 3x^2) + (3a + ax)

x^2(x+3) + a(x+3)

**(a + x^2)(x+3)**** **

Page 331 /56

**Factor the polynomial completely. If prime (cannot be factored), then say so.**

**z2 + 18z + 45**

z^2 + 15x +3x +45

**(z + 15)(z + 3)**** **

Page 331 /64

**Factor the polynomial completely. If prime (cannot be factored), then say so.**

**x2 − 5xs − 24s2**

x^2 –8xs +3xs –24s^2

**(x –8s)(x +3s)**** **

Page 331 /104.

**Factor the polynomial completely. If prime (cannot be factored), then say so.**

**− 4w3 − 16 w2 + 20w**

**(-2w^2 –10w)(2w –2)**** **

Page 332 /108.

__Area of a sail.__ A triangular sail has an area of x2 + 5x + 6 square meters and a height of x+3 meters. Find the length of the sail’s base. Refer to the picture in the text.

**The area of a triangle is **

A=x^2 +5x +6 while h=x +3

So x^2 +5x +6 = b(x +3)

= __x^2 +5x +6__ = __b(x +3)__

x +3 x +3

So x^2 +5x +6 /x +3 = b

If we divide x^2 +5x +6 by x +3 the answer is x +2

**So b = x+2 meters**** **

Page 338 /40

**Factor the trinomial using the ac method. Be sure to show steps showing this method.**

**15x2 − 7x − 2**

ac = 15 * -2

ac = -30

15x^2 – 10x + 3x – 2

(3x – 2)5 (3x – 2)x

**(3x – 2)(5x + 1)**** **

Page 338 /66

**Factor each trinomial completely using the trial-and-error method.**

(3x 1) (x 10) (3x 2) (x 5)

(3x 10) (x 1) (3x 5) (x 2)

**(3x – 2)(x – 5)** = 3x^2 – 17x + 10

Page 339 /102

**Factor the trinomial completely.**

**− 36a2b + 21 ab2 − 3b3**

b(-36a^2 + 21ab - 3b^2)

-3b(12a^2 - 7ab+ b^2)

**-3b (3a - b)(4a - b)**

Page 345 /32

**Factor the difference of cubes.**

**u3 − 125v3**

**(u – 5v)(u^2 + 5uv + 25v^2)**** **

Page 345 /66

**Factor the polynomial completely. If prime, say so.**

**32a 2 + 4a - 6**

2(16a^2 + 2a – 3)

2(2a + 1)(8a – 3)

**(4a + 2)(8a – 3)**** **

Page 345 /106

**Factor the polynomial completely. If prime, say so.**

**9bn3 + 15bn2 − 14bn**

bn(9bn^2 + 15bn – 14)

9 * -14 = -126

bn(9n + 21)(9n – 6)

**bn(3n + 7)(3n – 2)**** **

Page 353 /18

**Solve the equation.**

**2h2 − h − 3 = 0**

(2h – 3)(h + 1) = 0

2h – 3 = 0

2h = 3

h = 3/2

h + 1 = 0

h = -1

**Solutions are -1 and 3/2**** **

Page 353 /32

**Solve the equation**

**2w (4w + 1) = 1**

8w^2 + 2w = 1

8w^2 + 2w – 1 = 0

(2w + 1)(4w – 1) = 0

2w + 1 = 0

2w = -1

w = - ½

4w – 1 = 0

4w = 1

w = ¼

**Solutions are -1/2 and 1/4.**** **

Page 353 /44

**Solve the equation**

**m 3 + 2m 2 – 3m = 0**

m(m^2 + 2m - 3) = 0

m(m + 3)(m - 1) = 0

m = 0

m + 3 = 0

m = -3

m -1 = 0

m = 1

**Solutions are 0, 1, and -3.**** **

Page 353 /60

**Solve the equation**

__1 __h2 − __1 __h + 1 = 0

**18 2**

h^2 - 9h + 18 = 0

(h - 3)(h - 6) = 0

h – 3 = 0

h = 3

h – 6 = 0

h = 6

**Solutions are 6 and 3.**** **

Page 354 /96.

__Venture Capital. __Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation below where r is the average annual return:

** **

**12,000(1 + r)2 = 27,000**

12,000(1 + r)2 = 27,000

12,000 ( 1 + 0.50 ) = 27,000

**r = 50%**** **

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