Understanding Polynomials in Algebra

Polynomials are algebraic expressions that include real numbers and variables. Division and square roots cannot be involved in the variables. The variables can only include addition, subtraction and multiplication. Polynomials contain more than one term. Polynomials are the sums of monomials. A monomial has one term: 5y or -8x2  or 3.A binomial has two terms: -3x2  2, or 9y - 2y2A trinomial has 3 terms: -3x2  2 3x, or 9y - 2y2  y The degree of the term is the exponent of the variable: 3x2  has a degree of 2.When the variable does not have an exponent - always understand that theres a 1 e.g.,  1x Example of Polynomial in a Equation x2  - 7x - 6   (Each part is a term and x2  is referred to as the leading term.) Term Numerical Coefficient x2-7x-6 1 -7 -6 8x2 3x -2 Polynomial 8x-3 7y -2 NOT a Polynomial The exponent is negative. 9x2 8x -2/3 NOT a Polynomial Cannot have division. 7xy Monomial Polynomials are usually written in decreasing order of terms. The largest term or the term with the highest exponent in the polynomial is usually written first. The first term in a polynomial is called a leading term. When a term contains an exponent, it tells you the degree of the term. Heres an example of a three term polynomial: 6x2  - 4xy 2xy — This three term polynomial has a leading term to the second degree. It is called a second degree polynomial and often referred to as a trinomial.9x5  - 2x 3x4  - 2  Ã¢â‚¬â€ This 4 term polynomial has a leading term to the fifth degree and a term to the fourth degree. It is called a fifth degree polynomial.3x3  Ã¢â‚¬â€ This is a one term algebraic expression which is actually referred to as a monomial. One thing you will do when solving polynomials is combine like terms. Like  terms: 6x 3x - 3x NOT  like terms: 6xy 2x - 4 The first two terms are like and they can be combined: 5x2  2x2  - 3 Thus: 10x4  - 3 Now youre ready to start adding polynomials.

The Tragedy Of Macbeth By William Shakespeare - 1205 Words

The play of Macbeth is a tragedy which led to his demise. Macbeth was an honorable solider whose life became one of a traitor and a coward. The conflict of light and darkness within Macbeth began after he receives a prophecy from three witches that one day he will become King. This prediction without a doubt consumes him with ambition and greed. In order to fulfill the three witches prophecy Macbeth is led down his treacherous path by his wife, Lady Macbeth who urges him to murder King Duncan and seize the throne without hesitation. Macbeth struggle with his conscience and it was often difficult for him to differentiate between the illusion of ghost and what is real. Shakespeare uses the contrast of light and dark to provide readers a better understanding of good and evil within the play. The contrast of light and dark allows readers to understand characters morals and characteristic quickly and effectively. A glimpse of evil is first seen at the beginning of the play, â€Å"Fair is foul and foul is fair† (1.1.11). The darkness plays an important role in developing the conflict to understand Macbeth train of thoughts and what lead him to commit such heinous crimes. The darkness reveals his character or true self. We are all born with the choice to be good or bad and whatever opportunities are presented to us to further our ambition we will choose base on our morals. If an individual is able to get away with evil, then an attempt is made to do so as in the story of Macbeth.Show MoreRelatedThe Tragedy Of Macbeth By William Shakespeare1205 Words   |  5 PagesThe first tragic story created in ancient Greece. Tragedies were written as a form of catharsis or purgation of emotions. In these types of plays, the audience finds characters in which they can relate to w hich is a tragic hero. The tragic hero creates his own failures based upon their own actions and produces a detrimental fate for himself. The process of the protagonist’s fall is based upon the tragic structure. The structure of a tragedy consists of the exposition, exciting force, hamartia, theRead MoreThe Tragedy Of Macbeth By William Shakespeare892 Words   |  4 Pages‘The Tragedy of Macbeth’, written between 1599 and 1606 by William Shakespeare, has been reinterpreted in the 2010 film ‘Macbeth’. The 2010 film successfully takes its own reading of Shakespeare s play; by changing the setting, the director, Rupert Goold, effectively conveys many of the key themes and issues found in the original text. Whilst transforming some on the underlying meanings to correspond to the alternative readings contemporary audiences might take from Shakespeare s Macbeth. The objectiveRead MoreThe Tragedy Of Macbeth By William Shakespeare1724 Words   |  7 Pages As humans we are attracted to tragedy in our everyday lives. For the horror, understanding and contemplation of human nature what else can offer a better summary than Shakespeare? In the play the Tragedy of Macbeth by William Shakespeare the story progresses through the vision of the protagonist, Macbeth. Throughout the story Macbeth aspires to obtain more power than his original position, as sergeant, provides. With many dastardly deeds he achieves the position of king, although he becomes a tyrantRead MoreThe Tragedy Of Macbeth By William Shakespeare1023 Words   |  5 PagesWilliam Shakespeare is one the greatest writer of all time. Writing hundreds of books and scripts, Shakespeare founded his most success in his plays in the 1589-1613. One of his most popular plays is the Tragedy of Macbeth. The Tragedy of Macbeth was a turn from glory to tragedy. A story of a true tragic hero. Macbeth is a brave soldier in a war for Scotland. A tale of a great soilder that was highly prais e in his kingdom turn to a tragic murderous sinful king. Macbeth kill his friends and hisRead MoreThe Tragedy Of Macbeth By William Shakespeare1497 Words   |  6 PagesPractise Essay William Shakespeare effectively explores and follows the framework of the tragedy, Macbeth; a tale of systematic suffering, which foreshadows and imminently leads to the death of a great man. Essentially, it is Macbeth’s flaw – his growing ambition – which leads to these harsh repercussions. Shakespeare demonstrates his tragedy, through Aristotle’s elements and definition of tragedy, which ultimately concerns the reversal of good fortune to bad. In â€Å"Macbeth†, ambition conspires withRead MoreThe Tragedy Of Macbeth By William Shakespeare1090 Words   |  5 PagesThe Tragedy of Macbeth Literary Analysis In the play The Tragedy of Macbeth, William Shakespeare uses satire as tone and irony as points of view to portray Macbeth’s unfortunately placed ambition and the manipulation that is used on him. His ambition to gain a higher status as king ends with consequences to himself and the others in his path. Shakespeare adds dramatic irony, verbal irony, and situational irony to keep the readers at the edge of their seats as well as engaged in each lie and mishapRead MoreThe Tragedy Of Macbeth By William Shakespeare739 Words   |  3 PagesIn William Shakespeare’s play, The Tragedy of Macbeth, the Death of King Duncan of Scotland occurred at Thane Macbeth’s castle, Inverness, at around four in the morning in about the year 1300. Before the murder, Macbeth imagined seeing a bloody dagger floating before him, making it appear as if he was not totally sane. The reason the murder happened was because Macbeth had met three witches in the woods that prophesized to him that he would become king of Scotland. Afterwards, Macbeth sent a letterRead MoreThe Tragedy Of Macbeth By William Shakespeare972 Words   |  4 PagesIn the Tragedy of Macbeth, William Shakespeare utilizes a series of themes through the behaviors of many different characters. Some themes seen more clearly throughout the play are those of monarchy, tyranny, and gender. Perhaps the most prominent theme in the whole play is that of the â€Å"unsexing† of Lacy Macbeth’s character. Lady Macbeth wants to act in such a way that is not connected to her gender; we see this and how it relates to the plot and her part in both the rising action and climax in theRead MoreThe Tragedy Of Macbeth By William Shakespeare1052 Words   |  5 PagesEnglish II 2 October, 2015 â€Å"Tragedy† of Macbeth Macbeth, a play written by one of the most influential English writers of all time William Shakespeare. It was created to be a Shakespearean tragedy. A tragedy as Aristotle defines it as: â€Å"Tragedy, then, is an imitation of an action that is serious, complete, and of a certain magnitude †¦. through pity and fear effecting the proper purgation of these emotions† (Aristotle: Poetics). What this is saying for a tragedy is that it should have the audienceRead MoreThe Tragedy Of Macbeth By William Shakespeare1582 Words   |  7 Pagesto you and told you would be king would you trust them? Macbeth did and ultimately it led to his tragic demise. The tragedy of Macbeth was written by famous poet William Shakespeare in the earl sixteen hundredth. The play dramatizes the destructive physical and mental effects of radical ambition for people who seek authority for the benefit of an individual. Macbeth’s theme of ambition, lust for power, faith, and gullibility makes Macbeth his own antagonist, which is directly correlated to his death

Learning Team Charter Analysis Essay Example For Students

Learning Team Charter Analysis Essay Learning Team Charter Analysis Business Communications COM/285 August 02, 2010 Learning Team Charter Analysis Team A There are several key elements involved with establishing and maintaining effective communications in a group environment. Understanding the dynamics of group communication is essential at the outset of any project or endeavor that requires input from multiple team members. A great deal of thought should also be put into the process and ground rules for dispute resolution. As with any solid plan, the effective application of fundamental communications strategies coupled with leveraging available technologies will go a long way toward ensuring project success. Group communication is the communication that takes place while an ensemble of people, working together towards a goal; focus on the informational, procedural, and interpersonal dimensions of achieving that goal. A group may communicate differently throughout the three individual stages; formation, coordination, and formalization, of their task. Effective group communication is the key to a group’s ability to optimally plan, organize, and conquer their goal or task. The dynamics of group communication differ considerably from that of the communication that takes place throughout individual communication. Group communication involves dialogue, verbal or written, that is coming from, and intended for, more than two people, while individual communication is the dialogue which takes place between two people. Communicating effectively involves understanding your audience. In a group, this can pose as more of a challenge than with individual communication as there are likely different levels of understandings, thoughts, and communication styles amongst a group. When communicating in a group there is more opportunity for persons’ thoughts to go unsaid or unheard, while most individual conversations are reciprocal. In a group, it may be more difficult for some individuals to share their feelings of thoughts out loud and in front of a large group. Therefore, more efforts must be made to encourage participation. A goal in communication with another individual is that the dialog be a reciprocal. To encourage reciprocal conversations individuals can remember three simple rules; stop, look and listen. When participation in a conversation with another individual it’s important, when the other person begins talking, to stop and actively listen to what they are saying. Nodding your head or an occasional â€Å"uh-huh† shows them you are listening and helps that person feel that they are being taken sincerely. The strategies that are used to promote effective group communication are similar to those used when communicating with one individual; however, additional efforts are made to encourage equal involvement amongst members. Trust, cooperation, and productivity are all enhanced when a group practices effective communication. The communication within a group is most effective when all members contribute. A few strategies to promote participation are round robin, small group discussion, and brainstorming. Round robin is a method during which each member of a group is asked their thoughts on one specific topic, or question. Each team member then writes their responses down and all ideas and suggestions are then discussed openly. Small group discussion is a tool large groups can use to discuss intricate topics. The large group breaks apart into smaller groups to discuss the same topic. Each smaller group records what is conversed, summarizes and report back for further discussion. (Leister, 1992) Avoiding group think and identifying and addressing issues within the group is vital to the group’s ability to further communicate. Some strategies to promote group communication are that each member of the group is given a chance to give their input and that all thoughts are received with respect and understanding. A group strategy to overcome conflicts and challenges is that the group actively and openly listens to one another’s concerns and puts forth the effort to address and resolve them. University of Phoenix Learning Teams change with each new class. Team members could build a stronger Conflict Management section by modeling previous team charters where dispute guidelines are well developed. A sample charter reviewed by the Team had a statement that provided a good example for how disputes should be handled, â€Å"Active discussion, open-minded consideration, and mutual respect should support resolution of any conflicts† (Sample, 2010). This statement could be inserted into the beginning of the Conflict Management section to set a positive tone for how disputes should be handled. University of Phoenix classes span a five week period. The class timeframe limits the amount of possible conflicts that may arise between learning team group members. The submitted Learning Team A Charter provides minimal information for dispute resolution. The Team identified one possible source of conflict within the group; agreeing on topic or main points. Other sources of conflict could include late submission parts from team members and differences in opinion. The sample charter reviewed by Learning Team A listed non-participatory team members and misunderstandings as possible sources of conflict. By incorporating the additional four conflict sources into future charters, the Team names the five most common learning team problems. An effective Learning Team Charter should list specific strategies of dispute resolution for each conflict source. The charter for Learning Team A gave brief, but specific strategies for disagreements on topics and main points; team members could suggest option for topics and vote to settle the disagreement. Wiping the sweat from my brow I called a halt to the crew EssayAll their energy can be aimed in certain direction to achieve the common goal. The most detrimental and common problems of face to face meetings is groupthink. Many groups have dominating members and personalities. People are also so focused on agree that members will go along with the idea just to keep peace. (Locker, K; Kienzler, D, 2008) When this happens, the groups work runs the risk of becoming inferior or less than desired. Groupthink can be created by another issue of this type of group communication, the length of meetings. To avoid two and three hour processes, the members will suppress their comments and allow others to run ideas in the wrong direction. Sidebar conversations also take away from this setting. (Heathfield, 2010) Without total participation, meetings become unproductive and frustrating. Members often find themselves talking about work schedules, personal lives, and a host of other topics unrelated to the reason of the meeting. Another technology that can facilitate group meetings and mass communication is through email. The biggest advantage of email is the convenience of getting an idea out to many people at once. All the members of one team can get the same information simultaneously despite their location or time zone. Each member is also allowed to begin work immediately on their specific portion. Emails are date and time stamped which also enables the messages delivery to be verified. Some networks allow the sender to know when the receiver reads the message as well. Emails can be referred to and referenced at any time. When a members needs clarification on a thought they have the option to revisit the message and omit whatever part does not concern them. The sender of an email can also attached files that may assist other members with the work; all members can share and view the same information. The major disadvantage of an email is its dependence on the internet. Without a connection an email cannot be access and therefore rendered useless. Emails are also extremely impersonal and cold. It is very difficult to send emotion through email and members may become offended and shut themselves off from the process. Another major disadvantage the email is the possibility of a virus. Many messages have virus unintentionally attached to them that can crash a mailbox or the computer all together. Telephones can also be used to facilitate group communication. Telephones are the quickest way for group members to meet and pass ideas. This technique is less personal then face to face but offers a more personal feel than the email. If the member does not understand the information being given they can ask for clarification immediately and without the fear of backlash from other members. The top disadvantage of the telephone is the time zone consideration. Many teams are not locally assembled and are not available at the same time. This removes the opportunity for a teleconference and face to face meetings, leaving only email or individual phone calls to communicate. Many phones can distort or even delete frequencies due to quality. (Bowman, 2002) This is becoming more and more common with the use of cellular phones as opposed to landlines. People are more distracted with driving, family issues, and even television shows during phone conversation that again thoughts are not given complete thought. It’s clear to see that there can be many challenges associated with group communications. These challenges can also be intensified in an online working environment. This does not mean, however that effective communication cannot take place. Through the use and understanding of group dynamics, conflict resolution, proper planning strategies and available technology, it can be fairly easy to establish an effective communications plan. When a group of people recognize the important role that communication plays in the process of achieving their goals, they are well served to plan accordingly. References Leister, M. (1992). North Dakota State University. â€Å"Leadership Development within Groups – Communicating Effectively. † Retrieved July 30, 2010 from, http://www. ag. ndsu. edu/pubs/yf/leaddev/he499w. htm Gioia, C. (2010). â€Å"How to Start a Conversation and Make Friends. † Retrieved July 31, 2010 from, http://www. helium. com/items/537319 Schwartz, A. E. (July 26 2005). Clear Communication. Retrieved from http://ezinearticles. com/? clear-communication Communication is an exchange of information. It is a process of understanding on both the part of the receiver and the sender. Locker, K, Kienzler, D. (2008). Business and administrative communication. New York, NY: The McGraw-Hill Companies. Heathfield, Susan. (2010). Meeting management: deal with competing conversations . TIPS for working with people at work, Retrieved from http//:humanresources. about. com Bowman, Joel. (2002, August 24). Managing information and relationships. Business Communication, Retrieved from http://homepages. wmich. edu/~bowman/phone. html