Year 10 - Quadratic factorising - Free practice
Year 10 Quadratic Factorising Worksheets
Expand, factorise, difference of squares - the building blocks.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 10 expects students to fluently expand and factorise quadratics. These worksheets give the structured repetition needed to make the pattern recognition automatic - critical for VCE Methods.
What's covered
Sub-skills your student will practise
- ✓Expanding binomial products (FOIL)
- ✓Factorising x^2 + bx + c
- ✓Difference of two squares
- ✓Perfect-square trinomials
- ✓Mixed-format expand and factorise problems
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Frequently asked
Questions parents ask about quadratic factorising
What's the cleanest way to factorise a monic quadratic?
Find two numbers that multiply to the constant term and add to the x coefficient. For x^2 - 7x + 12: factors of 12 that add to -7 are -3 and -4. So (x - 3)(x - 4).
How do students factorise a non-monic quadratic?
Use the 'ac method' (or 'splitting the middle term'): for ax^2 + bx + c, find factors of ac that sum to b, then split bx into those two terms and factorise by grouping. Year 10A goes deeper into this.
What's perfect-square factorisation?
A specific pattern: a^2 + 2ab + b^2 = (a + b)^2 and a^2 - 2ab + b^2 = (a - b)^2. So x^2 + 6x + 9 factorises as (x + 3)^2. Recognising the pattern saves time on exam questions.
Why is fluent factorising so important in Year 10?
Because every Methods topic from now on assumes it - solving equations, sketching parabolas, finding intercepts, completing the square. Students who can't factorise fluently spend twice as long on every Methods question.
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