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Ashford 6: - Week 5 - 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. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.

Topics

Factoring

Read the following instructions in order to complete this discussion, and review the example of how to complete the math required for this assignment:

On pages 345, 346, and 353 of Elementary and Intermediate Algebra, there are many factoring problems. You will find your assignment in the following table.
Use your assigned number.

If your assigned number is	On Page 345	On Page 346	On Page 353
If your assigned number is	On Page 345	On Page 346	On Page 353	1	2	82	14
2	4	84	16
3	6	86	18
4	8	88	20
5	10	90	22
6	12	92	24
7	14	94	26
8	16	96	28
9	18	98	30
10	20	100	32
11	22	102	34
12	24	104	36
13	26	106	38
14	28	82	40
15	30	84	42
16	32	86	44
17	34	88	46
18	36	90	48
19	38	92	50
20	40	94	52
21	42	96	54
22	44	98	56
23	46	100	58
24	48	102	60
25	50	104	62
26	52	106	64
27	54	82	66
28	56	84	68
29	58	86	70
30	60	88	72
31	62	90	74
32	64	92	76
33	66	94	78
34	68	96	80
35	70	98	82
36	72	100	84
37	74	102	86
38	76	104	88
39	78	106	90
40	80	82	92

For the problems on pages 345 and 346, factor the polynomials using whatever strategy seems appropriate. State what methods you will use and then demonstrate the methods on your problems, explaining the process as you go. Discuss any particular challenges those particular polynomials posed for the factoring.

For the problem on page 353 make sure you use the “ac method” regardless of what the book’s directions say. Show the steps of this method in your work in a similar manner as how the book shows it in examples.

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.):
- Factor
- GCF
- Prime factors
- Perfect square
- Grouping

Your initial post should be 150-250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least a paragraph. Do you agree with how they used the vocabulary? Do their answers make sense?

my assigned number is #8.

INSTRUCTOR GUIDANCE EXAMPLE:

Week Five Discussion Factoring Since there are several different types of factoring problems assigned from pages 345- 346, four types will be demonstrated here to offer a selection, even though individual students will only be working two from these pages. #73. x3 – 2x2 – 9x + 18 Four terms means start with grouping x 2 (x – 2) – 9(x – 2) The common factor for each group is (x – 2) (x – 2)(x2 – 9)

Notice the difference of squares in second group (x – 2)(x – 3)(x -+ 3) Now it is completely factored. #81. 6w2 – 12w – 18 Every term has a GCF of 6 6(w2 – 2w – 3) Common factor is removed, now have a trinomial Need two numbers that add to -2 but multiply to -3 Try with -3 and +1 6(w – 3)(w + 1) This works, check by multiplying it back together #97. 8vw2 + 32vw + 32v Every term has a GCF of 8v 8v(w2 + 4w + 4) The trinomial is in the form of a perfect square 8v(w + 2)(w + 2) Showing the squared binomial 8v(w + 2)2 Writing the square appropriately #103. -3y3 + 6y2 – 3y Every term has a GCF of -3y -3y(y2 – 2y + 1) Another perfect square trinomial -3y(y – 1)(y – 1) Showing the squared binomial -3y(y – 1)2 Writing the square appropriately Here are two examples of problems similar to those assigned from page 353. 5b2 – 13b + 6 a = 5 and c = 6, so ac = 5(6) = 30. The factor pairs of 30 are 1, 30 2, 15 3, 10 5,6 -3(-10)=30 while -3+(-10)= -13 so replace -13b by -3b and -10b 5b2 – 3b – 10b + 6 Now factor by grouping. b(5b – 3) – 2(5b – 3) The common binomial factor is (5b – 3). (5b – 3)( b – 2) Check by multiplying it back together. 3x2 + x – 14 a = 3 and c = -14, so ac =3(-14)= -42. The factor pairs of – 42 are 1, -42 -1, 42 3, -14 -3, 14 2, -21 -2, 21 6, -7 -6, 7 We see that -6(7) = -42 while -6 + 7 = 1 so replace x with -6x + 7x. 3x2 – 6x + 7x – 14 Factor by grouping. 3x(x – 2) + 7(x – 2) The common binomial factor is (x – 2). (x – 2)(3x + 7) Check by multiplying it back together.