Factorising Quadratic Expressions - Splitting Down the Middle WORKSHEET
Suitable for Year groups: Year 10, Year 11
GCSE Tier: Higher
Targeting grades: 6-7
Prerequisite knowledge: Expanding brackets of linear expressions. Identifying common factors in algebraic terms. Recognising the structure of quadratic expressions. Factorising monic quadratics.
Learning Objective: Factorising quadratic expressions of the form a𝑥^2 + b𝑥 + c.
Factorising Quadratic Expressions - Splitting Down the Middle WORKSHEET DESCRIPTION
Provide students with structured practice in factorising quadratic expressions using the method of splitting the middle term.
Section A introduces straightforward grouping examples, such as x(x + 9) + 6(x + 9). Section B builds on this by applying the splitting method more directly, with expressions in the form 3x2 + 9x - 2x - 6.
Section C then challenges students to complete the whole process themselves. The gradual increase in difficulty ensures learners develop fluency with the technique and confidence in tackling a wide variety of quadratics.
If you're looking for other methods, check out our worksheet Factorising Quadratic Expressions – Using the Area Model (B).
Section A introduces straightforward grouping examples, such as x(x + 9) + 6(x + 9). Section B builds on this by applying the splitting method more directly, with expressions in the form 3x2 + 9x - 2x - 6.
Section C then challenges students to complete the whole process themselves. The gradual increase in difficulty ensures learners develop fluency with the technique and confidence in tackling a wide variety of quadratics.
If you're looking for other methods, check out our worksheet Factorising Quadratic Expressions – Using the Area Model (B).
All worksheets are created by the team of experienced teachers at Cazoom Maths.
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Frequently Asked Questions
Students should be comfortable expanding brackets of linear expressions and identifying common factors in algebraic terms before tackling this method. They'll also need to recognise the structure of quadratic expressions and have experience factorising monic quadratics, as these foundational skills are essential for successfully splitting the middle term.