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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

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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