Problem 4. Prove that (y^3+z^3 ) x^2+yz^4 is irreducible over C[x,y,z]. Also prove that (y^3+z^3 ) x^2+y^2 z^3 is irreducible. Assume that (y^3+z^3 ) x^2+yz^4=a*b. Then one of a or b is linear in x^2 and the other doesn’t have x^2 at all because the degree of the product is the sum of the two degrees. Now we write 〖a=cx〗^2+d, so c and d have only y’s and z’s. Then (y^3+z^3 ) x^2+yz^4=(〖cx〗^2+d)*b But now b*d=yz^4, and since C[y,z] is a unique factorization domain, b and d must be monomials. But this means b is a monomial, in y and z. Since b*c=y^3+z^3 and we see that y^3+z^3 factors to be (y+z)(y^2-yz+z^2). Since b is a monomial and b*c=(y+z)(y^2-yz+z^2) Then b must be either (y+z) or (y^2-yz+z^2). However, they must not have …show more content…
Guess: Res(x-a,f(x))= b_n a^n+⋯+b_1 a+b_0. Lemma: det[■(0&-a&0@⋮&⋮&⋮@■(0@b_n )&■(0@b_(n-2) )&■(0@b_(n-3) )) ■(…&0&0@…&⋮&⋮@■(…@…)&■(1@b_1 )&■(-a@b_0 ))]=b_n a^(n-1) Base Case: n = 2 det[■(0&-a@b_2&b_0 )]=0(-b_o )-b_2 (-a)= b_2 a n = 3 det[■(0&-a&0@0&1&-a@b_3&b_1&b_0 )]=0-(-a)(0(b_0 )-b_3 (-a))=b_3 a^2 Induction: Assume the determinant is b_n a^(n-1) is true for n≥3. Now look at n+1. det[■(0&-a&0@⋮&⋮&⋮@■(0@b_(n+1) )&■(0@b_(n-2) )&■(0@b_(n-3) )) ■(…&0&0@…&⋮&⋮@■(…@…)&■(1@b_1 )&■(-a@b_0 ))]=0-(-a)det[■(0&-a&0@⋮&⋮&⋮@■(0@b_n )&■(0@b_(n-2) )&■(0@b_(n-3) )) ■(…&0&0@…&⋮&⋮@■(…@…)&■(1@b_1 )&■(-a@b_0 ))] =a(b_(n+1) 〖(a〗^(n-1)))=b_(n+1) a^n Proof: Base Case is n = 2: det[■(1&-a&0@0&1&-a@b_2&b_1&b_0 )]=1*(1*(b_0 )-b_1*(-a))-(-a)*(0*(b_0 )-b_2 (-a)) =b_0+b_1 a+b_2 a^2 Induction: Assume for n≥2, det[■(1&-a&0@■(0@⋮)&■(1@⋮)&■(-a@⋮)@■(0@b_n )&■(0@b_(n-1) )&■(0@b_(n-2) )) ■(…&0&0@■(…@…)&■(0@⋮)&■(0@⋮)@■(…@…)&■(1@b_1 )&■(-a@b_0 ))]=b_n a^n+⋯+b_1 a+b_0 Now look at n+1. det[■(1&-a&0@■(0@⋮)&■(1@⋮)&■(-a@⋮)@■(0@b_(n+1) )&■(0@b_n )&■(0@b_(n-1) )) ■(…&0&0@■(…@…)&■(0@⋮)&■(0@⋮)@■(…@…)&■(1@b_1 )&■(-a@b_0 ))] =1*det[■(1&-a&0@■(0@⋮)&■(1@⋮)&■(-a@⋮)@■(0@b_n )&■(0@b_(n-1) )&■(0@b_(n-2) )) ■(…&0&0@■(…@…)&■(0@⋮)&■(0@⋮)@■(…@…)&■(1@b_1 )&■(-a@b_0 ))]-(-a)det[■(0&-a&0@■(0@⋮)&■(1@⋮)&■(-a@⋮)@■(0@b_(n+1) )&■(0@b_(n-1) )&■(0@b_(n-2) )) ■(…&0&0@■(…@…)&■(0@⋮)&■(0@⋮)@■(…@…)&■(1@b_1 )&■(-a@b_0 ))] 〖=1*(b〗_n a^n+〖=b〗_(n-1) a^(n-1)…+b_1 a+b_0+a(b_(n+1) a^n ) By
S: YMR stated that she had been living with her mother about one year, has is a newcomer. YMR lived with her maternal grandmother for many years back in her country. YMR stated that when she arrived to the U.S., she found out that her mother was pregnant, She shared that her mother did not want to tell her because she did not know how the client was going to react. YMR stated that she was happy because her mother had had four miscarries before. YMR explained that almost at the same time that she started living with her mother, the mother's partner and father of the child that her mother was going to have moved into her home. YMR stated that her mom used to work from 6am-12pm and the YMR spent a lot of time with her mother's partner. YMR stated that this man has
The facts of this case are that Dr. Guiles who is self-conscious of his prostate cancer diagnosis is treated horrendously when he finally decides to have surgery ( Buchbinder, Shanks & Buchbinder, 2014). Considering that Dr. Guiles is already sensitive about his condition, his unbearable symptoms are not helping matters (Buchbinder et al, 2014). Upon arrival at the hospital, he is treated subpar. The admitting clerk is rude and unbecoming to a patient who isn’t feeling well and who is embarrassed about his sickness (Buchbinder et al., 2014). To make matters worse, he has to find his own way up to the floor by walking, which causes him to be even later in checking in because of the need to stop frequently to urinate as well as having difficulty in walking (Buchbinder et al., 2014). Once he arrives on the floor, the charge nurse is not welcoming and unprofessional (Buchbinder et al., 2014). After figuring out what to do with the paperwork; and the nurse aide delivers Dr. Guiles to his room, the nurse aide does not offer to help settle him in (Buchbinder et al., 2014). Therefore, Dr. Guiles is faced with battling obnoxious family members who are on his bed and to make matters worse someone is in the bathroom which doesn’t help his need of having to frequently urinate (Buchbinder et al., 2014). When the issues are brought up to the charge nurse, the charge nurse accuses Dr. Guiles of wanting preferential treatment
This type of research is very valuable. This type of research is the most accurate and best way to fully understand the virus. It may be time consuming but it is the best way to study the virus.
Mark volunteered to help with the community arts festival; he was supporting the not-for-profit organization as he had in the past. However, he did not know his good intentions as a volunteer would cost him his job as an assistant manager. The retail store’s phone number was printed in the festival advertising in error and ticket requests overloaded the phone lines, causing loss of business and annoyed the store manager. As a result, Mark was seen as the cause of the problems and terminated.
When given a set of numbers, Brandon is able to count by 2's, 5's, and 10's to 100 with about 75% accuracy. Brandon has worked very hard his quarter and shown great improvements when telling time to the nearest 5 minutes. Addition facts have been a challenge for Brandon this quarter. He is able to answer addition facts that include +0, +1, and some +2. In order to answer all other addition facts, Brandon has been using the counting-up strategy. Brandon has been diligently working on learning and remember more of his addition facts. Brandon is becoming more consistent when asked to name and state the value of each coin.
As we have learned in Scenario # 4, Jeff and Elena file as MFJ, combining their income and forms 1095-A. Since Elena got married during the year she wants to claim the “Alternative Calculation” on Form 8962 for months prior to the marriage. She doesn’t want to pay back the $138 calculated in Scenario #4.
Power in numbers was the theme at Pig & Prince where Israel Cronk, Director of the Montclair Business Improvement District (BID), hosted a meet and greet. Local entrepreneurs came out to make friends, provide suggestions, join an ad-buy program designed to provide advertising at competitive prices, and to network, while volunteers and community organizers were recognized for their efforts.
Case Name The Smithson’s Mortgage Case Study Teams This case is designed to be conducted by a team of students. The discussion, questioning, and resolution of differences is an important part of the learning experience. Another significant advantage is the sharing of the workload in preparing the final case study report. Knowledge Background This case draws heavily on the material presented in Chapters 2 and 3 of Principles of Engineering Economic Analysis, 4th Edition by White, Case, Pratt, and Agee, particularly Section 3.4 (Principal Amount and Interest Amount in Loan Payments). To a limited extent it draws on concepts from Chapter 4 (Measuring the Worth of Investments), Chapter 5 (Comparison
In reading the first article Coach Knight: The Will to Win, I found the article found Coach Knight to be very offensive and mean to his players. Coach Knight did not display good leadership skills. According to the article, Coach Knight’s drive and passion for excellence was not always received as well as his record of wins and losses Snook, Per low, Delacey, 2005).
This case discussed the events that occurred during a change in DSS Consulting’s organizational structure. Three retired school district administrators established DSS Consulting during the late 1990’s. The company offered administrative support to small school districts located within the mid-west and mountain west region. They specialized in handling the negotiating of labor agreements as well as implementation of permanent system solutions designed to enable those organizations to run efficiently.
This case problem is related to a property purchase strategy. The president of Oceanview is deciding whether to bid for a property to build and sell condominiums. However, this depends on whether the state can change the zoning of the property to permit construction of condominiums. Here, the decision is whether to bid for the property, and chance events are firstly, whether the bid can be successful, and secondly, whether the state will approve the zoning change. To assess the likelihood that the state will approve the zoning change, the president can hire a market research service. Hence, the president is facing another decision as
Tired of trying to take his mind off the problem by focusing on the distant horizon, Hargrove was exploring the galley when Sanchez, his counterpart in sales, had walked in.
2. Compare this research design with a survey research design. What advantages, if any, did this research design have over a survey?
Tale servizio, offerto da Tyring, prevede la sostituzione del battistrada consumato con del materiale nuovo,
Mr. Alfaro Burgos, the vice president for sales of Dyners Corporation. It is a family firm that manufactures stainless steel and silver plated tableware. After some time, the inventory of the company showed a shortage. He discovered some mispacking of silver plated tableware in the warehouse of the corporation. He hired an industrial security firm to investigate the deprivation in the warehouse. It did not take long for the agent to discover the truth. Karlo Deles, the warehouse supervisor was the man behind the internal