Factorisation

Summary and Exam Tips for Factorisation

Factorisation is a subtopic of Algebra, which falls under the subject Mathematics in the Cambridge IGCSE curriculum. Factorisation involves breaking down an algebraic expression into simpler components by identifying and extracting common factors. The process is essentially the reverse of expansion, where the goal is to simplify expressions by taking out the Highest Common Factor (HCF).

For example, in the expression $6x^2 + 2xy - 8xz$, the common factor $2x$ is extracted to give $2x(3x + y - 4z)$. Similarly, factorising quadratics like $x^2 + 11x + 24$ involves finding two numbers that multiply to 24 and add to 11, resulting in $(x+3)(x+8)$.

The process often requires dividing terms into pairs to identify common factors, as seen in $18mx - 3nx + 12my - 2ny$, which simplifies to $(3x+2y)(6m-n)$. Mastery of factorisation is crucial for solving algebraic equations efficiently and is a fundamental skill in algebra.

Exam Tips

• Understand the Basics: Ensure you are comfortable with the concept of expansion and how factorisation is its reverse. This understanding is key to mastering algebraic expressions.

• Identify Common Factors: Always look for the HCF in each term of the expression. This is your first step in simplifying the expression.

• Practice Pairing Terms: When dealing with complex expressions, practice dividing them into pairs to make factorisation easier.

• Quadratic Factorisation: For quadratics, remember the two-step process: find numbers that multiply to the constant term and add to the linear coefficient.

• Practice Regularly: Use practice questions and past papers to hone your skills. The more you practice, the more intuitive factorisation becomes.