2 Algebra
In this chapter we review the basic principles of algebra in some detail and introduce some
more advanced topics. There is a lot of work in this chapter, reflecting the importance of
algebra, but don’t feel you have to do it all at once. Some topics, such as the binomial
theorem, you may like to leave until you need them.
Prerequisites
It will be helpful if you know something about:- the rules of arithmetic (10
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)- the properties of zero (6
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)- algebraic manipulation of symbols
- powers and indices (18
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)- factorial notation (16
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)Objectives
In this chapter you will find:- multiplication of linear expressions
- addition and multiplication of simple polynomials
- factorisation of polynomials by inspection
- simultaneous linear equations
- definition and use of identities
- factors and roots of a polynomial and use of the factor theorem
- rational functions and their properties
- addition and multiplication of rational functions
- division of polynomial expressions and use of the remainder theorem
- partial fractions
- properties of quadratic expressions and equations
- powers and indices for algebraic expressions
- the use of the binomial expansions of(a+b)nand( 1 +x)nfor positive integern
Motivation
You may need the material in this chapter for:- manipulation of mathematical expressions of scientific and engineering relationships