Factorisation

Summary and Exam Tips for Factorisation

Factorisation is a subtopic of Algebra, which falls under the subject Mathematics in the IB MYP curriculum. Factorisation involves breaking down expressions into products of simpler factors, essentially the opposite of expansion. For instance, the expression $12my - 2ny + 18mx - 3nx$ can be factorised as $(3x+2y)(6m-n)$. A common strategy is to divide terms into pairs before factorising.

When dealing with quadratic equations like $x^2 + 11x + 24$, the goal is to find two numbers that multiply to the constant term and add to the linear coefficient. For equations where the quadratic term's coefficient isn't 1, such as $ax^2 + bx + c$, the process involves finding numbers that multiply to $a \times c$ and add to $b$, then splitting and factorising accordingly.

The difference of two squares is another technique, where expressions like $x^2 - y^2$ are factorised as $(x+y)(x-y)$. For example, $x^2 - 16$ becomes $(x+4)(x-4)$. Practice problems often involve completing the square or fully factorising expressions like $2x^2 - 4x - 6$, which simplifies to $2(x+1)(x-3)$.

Exam Tips

• Understand the Basics: Ensure you grasp the fundamental concept that factorisation is the reverse of expansion. This understanding will help you identify common factors quickly.
• Practice Pairing Terms: When factorising, especially in complex expressions, practice dividing terms into pairs to simplify the process.
• Quadratic Equations: For quadratics, remember to find two numbers that multiply to the product of the quadratic term's coefficient and the constant term, and add to the linear term's coefficient.
• Difference of Squares: Familiarise yourself with the difference of squares formula $(x^2 - y^2 = (x+y)(x-y))$ as it frequently appears in exams.
• Check Your Work: Always verify your factorisation by expanding the factors to ensure they match the original expression. This step helps catch any errors.