AQA · Mathematics · 8300
GCSE Maths: Factorisation: quadratics harder
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Factorisation: quadratics harder (Corbettmaths Video 119), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the factorised form of x² + x − 6?
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(x + 3)(x − 2)
What is the factorised form of x² − 121?
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(x + 11)(x − 11). This is a difference of two squares.
What is the factorised form of y² − 9w²?
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(y + 3w)(y − 3w). This is a difference of two squares with two variables.
What mistake did Freddy make when he factorised x² − 11x + 30 as (x + 5)(x + 6)?
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He used the wrong signs. The correct factorisation is (x − 5)(x − 6), since both factors must be negative to give a positive product (+30) and a negative middle term (−11x).
What is the fully factorised form of 2y² − 50?
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2(y + 5)(y − 5). First factor out the common factor 2 to get 2(y² − 25), then recognise the difference of two squares.
What is the factorised form of 2x² + 5x + 2?
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(2x + 1)(x + 2)
What is the factorised form of 3y² + 10y − 8?
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(3y − 2)(y + 4)
What is the factorised form of 7x² + 8x + 1?
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(7x + 1)(x + 1)
What is the factorised form of 3x² + 4xy + y²?
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(3x + y)(x + y)
What is the fully factorised form of (x + 4)² + 3(x + 4)?
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(x + 4)(x + 7). Factor out the common term (x + 4) to get (x + 4)[(x + 4) + 3] = (x + 4)(x + 7).
If 10x² + 9x + 2 factorises as (5x + 2)(2x + 1), what is the factorised form of 10(y − 3)² + 9(y − 3) + 2?
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(5(y − 3) + 2)(2(y − 3) + 1) = (5y − 13)(2y − 5). Substitute (y − 3) for x in the factorised form, then simplify.
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