Submitted By Abdol007
Words 668
Pages 3
Exercise: Expand and simplify

2 x−

1 x

3

Think Quick: . Factorize 10x2 y − 6xy 2 .
See Example 1.16 on page 17.

Factorizing Quadratics Key: x2 + (α + β)x + αβ = (x + α)(x + β) Basic Factorization Factorization is all about ﬁnding factors.
Turn back to the bottom of page 16.

Note. You will have learned a technique for applying this result at school. Revise it!

Example Factorize 6x2 + 17x + 12.

Standard Factorizations The following are handy to remember.

• a3 ± b3 = (a ± b)(a2 ∓ ab + b2 ) • an − bn = (a − b)(an−1 + an−2 b + . . . + abn−2 + bn−1 )

Exercise: Factorize the following 1. −5m3 − 10m2

2. 16x4 − y 4

Algebraic Fractions Exercise: 3. a3 + a2 − a − 1 Recall:

• To simplify a fraction, factorize the numerator and denominator, then cancel out any common factors.

• To add/subtract fractions, ﬁnd a common denominator. Express all frac4. 5x2 − 7x − 6 Note. tions with that common denominator, then add/subtract the numerators.

c a+c a + = b d b+d

Examples 1.

x x+y 3x + 6 6x + 12

Exercise: Simplify the expression

2.

3 x 2 − + . x − 2 x x2 − 3x + 2

3.

2 1 − x − 1 x2 − 1

You should do Exercises 1.3.2, Questions 11-15.

1.3.3 Equations, inequalities and identities Solving Equations
Turn to page 20.

Exercise: Solve the equation

7 6 = . 1 − 2x x−2

Solving linear equations is a skill you should have already mastered.

Think Quick: Solve

1 = 1 for t. t−5

Solving equations that arise from worded problems is a skill you should continue to practice.
See Example 1.19 on page 20.

Example

2x + 3x2 − 7 = 0

ax2 + bx + c = 0 where a, b, c ∈ R, a = 0.

There are two main methods for solving quadratic equations:

• formula • factorisation
See equation (1.8)…...

### Similar Documents

#### Critical Review of the Article “the Changing Body of Students - a Study of the Motives, Expectations and Preparedness of Postgraduate Marketing Students”

...changing body of students - A study of the motives, expectations and preparedness of postgraduate marketing students” The fact is that the body of postgraduate marketing students, who decide to study in UK, has become much more different during the last few years. It means that British marketing educators are facing big challenges as well as great opportunities. In order to help the educators keep up with the pace of the change, researches about the postgraduate marketing students have been conducted. According to Liu (2010), the article - “The changing body of students - A study of the motives, expectations and preparedness of postgraduate marketing students” aims at finding out the possible implications for the educators by evaluating the motives, expectations and preparedness of the postgraduate marketing students in UK, and through this, the marketing educators could design their programme better. This paper will try to analyse the article and give a critical review for it. Even facing with the challenges from counterparts such as American universities and Asian domestic universities (Liu, 2010), the trend is that numbers of the postgraduate students in UK including those, who major in marketing, have still increased dramatically. More students choose to take a postgraduate programme in UK, particularly on taught programme (Liu, 2010). Taylor (2002) states that comparing with undergraduates, numbers of postgraduates......

Words: 1146 - Pages: 5

...Postgraduate Education in the United Kingdom Higher Education Policy Institute and The British Library Ginevra House January 2010 Contents Section Introduction Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Purpose and arrangement of this study What is postgraduate education? Who studies for postgraduate qualifications? Trends in postgraduate study Institutional differences and regional disparities Costs and benefits International standards and quality Future demand Page 1 3 9 24 40 47 59 63 2 Introduction: Purpose and arrangement of this study 1. The purpose of this study is to provide an overview of the postgraduate education sector in the UK, bringing together published data and reports in a convenient format and highlighting areas that may be of interest to policymakers. It provides a continuation and extension of the Higher Education Policy Institute’s (HEPI) previous report on postgraduate education in the UK published in 2004.1 2. This report mostly looks at the sector from a UK-wide perspective, unless dealing specifically with regional differences. However, since the large majority of the students in higher education are registered in English universities, this only gives us a clear picture of what is happening in England and does not necessarily reflect the situation in Scotland, Wales and Northern Ireland, or indeed any one of the nine English regions. The reader should bear in mind that many of the discussions focus mainly on...

Words: 22770 - Pages: 92

Free Essay

#### The Body of Students

Words: 10190 - Pages: 41

Free Essay

#### The Changing Body of Students

...The changing body of students A study of the motives, expectations and preparedness of postgraduate marketing students Jie Liu Department of Business and Management Studies, Manchester Metropolitan University, Manchester, UK Abstract Purpose – The aim of this paper is to assess the motives, expectations and preparedness of postgraduate marketing students, and discuss possible implications for postgraduate marketing education in the UK. Design/methodology/approach – The research uses primary data collected from postgraduate marketing students at four British universities. Factor analysis is used to evaluate the convergent validity of the survey questionnaire and Cronbach’s alpha coefficient to examine the internal consistency and reliability of the variables composing the major scales. Findings – The results indicate that postgraduate marketing education today faces a culturally diverse student body coupled with a notable lack of relevant work experience. Students are found to have relatively low perception of their preparedness for postgraduate study and high expectations for support and practical experience in marketing. Research limitations/implications – The sample used is relatively small although the high response rate achieved would help add validity to the study. Further research should examine the ways in which students draw on their prior-learning experience to make sense of their learning process. Practical implications – This study should...

Words: 2112 - Pages: 9

#### Motivation

Words: 297 - Pages: 2

#### Blahblahblah

Words: 1613 - Pages: 7

Free Essay

Words: 5434 - Pages: 22

#### Differences in Travelling Preferences

...The differences in travelling preferences between postgraduate students in Poland and United Kingdom Module name: Research Methods Word count: 4978 January 2014 1. Abstract The purpose of this report is to determine the differences between travelling preferences among British and Polish postgraduate students. Moreover, the report aims to establish the patterns in which a cultural background influence travelling and to detect similarities between British and Polish attitudes. Therefore, the research is a comparative, cross-cultural study. In order to achieve the purpose, 5 structured interviews were carried out that helped to construct a questionnaire. The analysis of qualitative and quantitative data shows that the cultural background has an effect on postgraduate students' travelling preferences and that there are certain differences between British and Polish travelling tendencies. The particular aspects that affect those preferences are: language, socioeconomic status, geographic area and customs. However, owing to the global phenomena, the cultural backgrounds are disappearing and students' travelling preferences become more and more convergent. The author believes this research will form a valuable asset for tourism industry and it will be a base for future research. 2 2. Table of contents 1. Abstract ......................................................................................................................................................

Words: 8325 - Pages: 34

#### Planning and Reflection Skills at Postgraduate Level

Words: 3289 - Pages: 14

Free Essay

#### Review

...Management System and Performance Improvement Plan, which reflects a better process in the execution. During his first 8 months working at SapuraKencana, he managed to complete the reflagging of two vessels that has been standing for a year, worked closely with Human Resource department. Sometime around 2010, Mr. Ameirul Azraie used to volunteer his will to participate in Dr. Azizan’s Seminar. He learned every inch of aspects on how to organize corporate events and marketing business until 2012, he and his partner advocate an event or a talk on how to write a Curriculum Vitae (CV) and also at the same year, he and his partner registered his company at Suruhanjaya Syarikat Malaysia (SSM) and became Malaysian Postgraduate Workshop Series (MPWS) Enterprise to Malaysian Postgraduate Workshop Series a year later. Achievement During his days at University Teknologi Petronas, he has been doing his internship as Trainee Engineer at Carigali Hess Operating Company Sdn. Bhd from December 2007 to July 2008 for 8 months. He managed to solve a Phase 2 Project Hook-Up & Commissioning (HUC) of Bumi-A (SYA) & Bulan-A (BLA) Flowlines by managing HUC Contractor’s work and executive plans, encountering the execution of Work Oder and Management of Change (MOC) and also performed technical-commercial bid evaluation based on required specifications and standards. On August 2009 to August 2010, he graduated as a Trainee Piping Design Engineer at Technip Company in accordance of Skill......

Words: 1231 - Pages: 5

Free Essay

#### Thesis Guide

Words: 12383 - Pages: 50

#### Dfds

...Reflector or Theorist? In Search of Postgraduate Learning Styles in Tourism and Hospitality Education Rong Huang (rong.huang@plymouth.ac.uk) and Graham Busby (gbusby@plymouth.ac.uk) University of Plymouth, Plymouth Business School, Plymouth, Devon PL4 8AA ©Journal of Hospitality, Leisure, Sport and Tourism Education Abstract Provision of higher education for international students has become an important source of income for British universities. These students have attracted some research attention. This paper considers the learning styles adopted by postgraduate students at one British higher education institution. It is based on their approaches to a specific assignment relating to Krakow, Poland, and utilises multiple methods of data collection. Results from utilising the Learning Styles Questionnaire are presented and tentative conclusions drawn. It is argued that a didactic approach is not sufficient on its own and that assignments need to play to the individual’s personal characteristics where possible. Keywords: Learning styles; International students Introduction The provision of education and training services for people from overseas has become an increasingly important source of income for certain countries, including the UK (Mazzarol, 1998; Mazzarol and Soutar, 1999; 2002). International and particularly non-EU students have inevitably attracted attention from academics in various subject areas. There were 74,235 international students (UKCOSA, 2006) who......

Words: 1682 - Pages: 7

#### Innformation and Knowledge Management

Words: 24199 - Pages: 97

Free Essay