S3 Maths: Factorising Quadratic Expressions (Paper 4 (error Clinic))

S3 Maths: Factorising Quadratic Expressions (Paper 4 (error clinic))

2026-11-14

Tutor Prep Guide · Taking out common factors, difference of two squares, perfect squares and cross multiplication, factorising quadratic trinomials over the integers and checking the result

S3 Maths: Factorising Quadratic Expressions (Paper 4 (error clinic))

Paper 4 (error clinic): ten questions on factorising quadratic expressions, with answers and one line notes.

Direct answers　Level: S3 maths; format: factorisation questions using common factors, difference of squares, perfect squares and cross multiplication.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	20
Difficulty mix	Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1
Chapter	Chapter: S3 Maths: Factorising Quadratic Expressions
Level	S3

02　Questions (10 items)

FoundationFactorise x squared minus 1.
FoundationFactorise 7x squared plus 14x.
FoundationFactorise x squared minus 6x plus 9.
IntermediateFactorise x squared plus 2x minus 15.
IntermediateFactorise 10x squared minus 5x.
IntermediateFactorise x squared minus 36.
ChallengeFactorise 3x squared minus 10x plus 8.
ChallengeFactorise 2x squared plus x minus 6.
ChallengeIf (x + a)(x + b) equals x squared plus 11x plus 30 and a is less than b, find a and b.
Error redoError clinic: a student factorises 3x squared plus 6x as 3 times the quantity x squared plus 6x. What is correct?

03　Answers and one-line notes

#	Answer	One-line note
1	(x + 1)(x – 1)	1 is 1 squared, the simplest case of a difference of squares.
2	7x(x + 2)	The common factor is 7x, leaving x plus 2 inside the bracket.
3	(x – 3) squared	The first term is x squared and the last is 3 squared, and twice x times 3 gives the negative middle term 6x.
4	(x + 5)(x – 3)	The numbers multiply to minus 15 and add to 2, namely 5 and minus 3.
5	5x(2x – 1)	The common factor is 5x, leaving 2x and minus 1 in the bracket.
6	(x + 6)(x – 6)	36 is 6 squared, so the difference of squares gives the answer directly.
7	(3x – 4)(x – 2)	Expanding gives 3x squared minus 6x minus 4x plus 8, and the middle terms add to minus 10x.
8	(2x – 3)(x + 2)	Expanding gives 2x squared plus 4x minus 3x minus 6, and the middle terms add to x.
9	a = 5 and b = 6	The numbers multiply to 30 and add to 11, namely 5 and 6, with the smaller one as a.
10	3x(x + 2)	The common factor must be taken out completely, so x comes out as well and the bracket becomes x plus 2.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

Take out any common factor first, then count the terms: two terms point to a difference of squares, three terms to a perfect square or cross multiplication. Always expand the answer to check the middle term.Tutor Registration →

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