Factorisation means writing an algebraic expression as a product of two or more factors. This chapter builds the skill in stages.

  • Highest Common Factor (H.C.F) of monomials: the common factor with the greatest co-efficient and the highest powers of the letters that every term shares.

  • Introduction to factorisation: what it means to write an expression as a product of factors.

  • Algebraic identities: standard results such as a2−b2=(a+b)(a−b)a^2-b^2=(a+b)(a-b) and a3+b3=(a+b)(a2−ab+b2)a^3+b^3=(a+b)(a^2-ab+b^2), used to factorise harder expressions.

  • Splitting the middle term: factorising a quadratic expression of the form ax2+bx+cax^2+bx+c.

  • Division of algebraic expressions: factorisation put to work in division, in four steps:

    • a monomial by a monomial;

    • a polynomial by a monomial;

    • a polynomial by a polynomial, using factorisation;

    • a polynomial by a polynomial, using long division or a shortcut method.

Each stage rests on the one before it. Finding the H.C.F of monomials is the first step, because taking out a common factor is the simplest kind of factorisation, and every later method comes back to it.