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 is essentially the reverse process of expansion, focusing on extracting common factors from expressions. For example, in the expression $12my - 2ny + 18mx - 3nx$, factorisation involves grouping terms to reveal common factors, resulting in $(3x + 2y)(6m - n)$.

When dealing with quadratic equations, factorisation requires identifying two numbers that multiply to give the product of the quadratic term's coefficient and the constant term, and add to give the linear term's coefficient. For instance, in $x^2 + 11x + 24$, the numbers 3 and 8 satisfy these conditions, leading to the factorised form $(x+3)(x+8)$.

For quadratic equations where the coefficient of $x^2$ is not 1, such as $6x^2 + x - 2$, the process involves finding numbers that multiply to the product of the leading coefficient and the constant term, then splitting the middle term accordingly. This results in factorisation by grouping, yielding $(2x-1)(3x+2)$.

The difference of squares is another key concept, where expressions like $x^2 - y^2$ are factorised as $(x+y)(x-y)$. This method is particularly useful when dealing with quadratic terms and constants that are perfect squares.

Exam Tips

• Understand the Basics: Remember that factorisation is the reverse of expansion. Always look for common factors first.
• Quadratic Equations: For quadratics, identify two numbers that multiply to the product of the quadratic term's coefficient and the constant, and add to the linear term's coefficient.
• Difference of Squares: Recognize expressions that fit the pattern $x^2 - y^2$ and apply the formula $(x+y)(x-y)$.
• Practice Pairing: Sometimes, you may need to rearrange terms into pairs to simplify factorisation.
• Check Your Work: After factorising, expand the factors to verify that you return to the original expression. This ensures accuracy.