Week 1 – Discussion 1

 

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses.

 

     

Domains   of Rational Expressions

Domains of Rational Expressions

In this discussion, you are assigned two rational expressions to work on. Remember to factor all polynomials completely. Read the following instructions in order and view the example to complete this discussion. Please complete the following problems according to your assigned number. (Instructors will assign each student their number.)

   

If   your assigned number is:

Your   first rational expression is

Your   second rational expression is

 

1

a2   + 2a – 10
  –11a

2x   – 8
  x2 – x

 

2

y2   + 11y + 30
  y + 5 

5a   – 3
  a2 – 49 

 

3

u2   + u – 72
  3u – 15

2w   – 1
  w2 – 9 

 

4

x2   – 6x – 55
  x2 – 3x – 28

b   – 3
  4b2 – 16 

 

5

16b2   – 1
  2b2 + 11b – 6

c2   + 2c – 10
  10c2 – 80c + 160

 

6

4w2   – 9
  –5w

y2   – 4
  2y2 + y – 1

 

7

a2   + 6a + 9
  a – 10

t2   + 2t – 10
  t2 – 6t + 8

 

8

81m2   – 16
  5m + 10

22x   + 11
  2×2 – x

 

9

3a2   + 16a + 5
  a2 – 7a + 10

b2   + 7b + 10
  b2 – 9 

 

10

4×2   – 1
  6x – 18 

r2   + 2r – 24
  r – 2 

 

11

t2   – 14t + 49
  4t – 8

3q2   – 22q + 24
  q2 – 1

 

12

v2   – v – 20
  v2 + 4v + 3

6t   – 3
  t 

 

13

n2   – 2n  – 15
  n – 2

8k   + 6
  8k2 + 2k – 3 

 

14

64k2   – 9
  2

s2   + 2s – 15
  s2 – 36 

 

15

4k2   – 12k + 9
  4k

3w2   + 36
  2w – 8 

 

16

5m2   + m
  m + 6

12a   – 15
  5a – 25 

 

17

7t2   – 14t
  4t2 – 9

36   – w2
  w 

 

18

22x   + 11
  x2 – 3x – 10

1   – 2c
  20c2 + 10c 

 

19

20c3   + 5c2 – c
  7c – 14

3a2   – 12a  
  24a2 – 18a

 

20

g2   – 36
  6g2 + 15g

7n   – 2
  4n2 – 25

 

21

1   – 2x + x2
  x2 – 1

2c2   + 5c – 25  
  14c – 21 

 

22

144   – w2
  8 – 2w

z2   – 8z + 16
  –12

 

23

4   + 16n2
  n – 8

3×2   – 2x – 1  
  x2 – 81

 

24

y2   – 25
  –6y

     37       
  2p – 4p2

 

25

a2   – 100
  a2 + 5a + 6

3b2   – 9  
  b – 8 

 

26

1   – x2
  x2 + 10x + 25

2u   – 2
  1 – u 

 

27

3z   + 3
  3z

5y3   – 75y
  2y2 + y – 15 

 

28

9   – 36×2
  8

15k2   – 5k
  k2 – k – 30

 

29

x2   – 7x + 12
  5x

w2   – 9w – 36  
  16w2 – 1

 

30

m2   + 13m + 40
  6m

4y   – 3
  25y2 – 4 

 

31

k2   – 8k
  17

2b   + 1  
  3b2 – 12 

 

32

9b2   + 3
  41

2x   – 6
  10×2 + 5x 

 

33

15×2   + 45
  50x

42
  m2 – 3m  

 

34

g2   + 46g
  g

3k   + 1
  k2 + k – 42 

 

35

4a   – 5
  14

4m3   +16m
  3m2 – m

 

36

x2   – 25
  23

b2   – 18b + 81
  3b2 – 12

 

37

9m2   – 4
  23

5x   + 15
  x2 – 49 

 

38   

d2   + 9
  33

m2   + 4m – 5
  5m2 + m

 

39   

13n2   – 13n
  6n

2w   + 1
  9w2 – 1

 

40

4×3   – 16
  x

14   
  2b2 – 8  

 

41

x2   + 2x – 10
  3x

2x   – 8
  x2 – 7x + 10

 

42

x2   + x – 72
  24

5b   – 3
  b2 – 4 

 

43

w2   + 11w + 30
  7w

2n   – 1
  4n2 – 9

 

44

g2   – 6g – 55
  g

k3   + k
  k2 – k – 42 

 

45

16t2   – 1
  64

x2   + 2x – 10
  3x – 15

• Explain in your own words what the meaning of domain      is. Also, explain why a denominator cannot be zero.
• Find the domain for each of your two rational      expressions.
• Write the domain of each rational expression in set      notation (as demonstrated in the example).
• Do both of your rational expressions have excluded      values in their domains? If yes, explain why they are to be excluded from      the domains. If no, explain why no exclusions are necessary. 
• Incorporate the following five math vocabulary words      into your discussion. Use bold font to emphasize the words in your      writing. Do not write definitions for the words; use them appropriately in      sentences describing your math work.
  • Domain 
  • Excluded value 
  • Set
  • Factor
  • Real numbers

Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7. Is their work similar to your own? Did they use the vocabulary words correctly? Do you understand their answers? 

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.