We move from numbers to letters. Using letters in place of numbers lets us write general rules, valid for any value: this is the heart of algebra. The chapter starts from the elementary building blocks — monomials and polynomials — and their operations, then tackles special products, those formulae that recur so often that they are worth learning by heart. From there we reach the core of literal calculus: factorisation, with all its techniques (factoring out a common factor and partial factoring, difference of squares, the special trinomial, sum and difference of cubes, Ruffini’s rule). The chapter closes with polynomial division and the computation of the GCD and LCM of polynomials, tools we shall need for equations, inequalities and algebraic fractions.
Sections
- Monomials
- Polynomials
- Special products
- Factorising polynomials
- Polynomial division and Ruffini’s rule
- Partial factoring
- GCD and LCM of polynomials