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Junior Cycle · Junior Cycle Maths

Junior Cycle Maths: Factorising

How often Factorising comes up on the Maths papers, every year it was asked, and questions to try.

HL Asked on 3 of the last 5 Higher Level papers, most recently in 2024. most years

OL Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Factorising, Higher Level(7 marks)

Quick ones on Factorising.

(a)Factorise x² − 5x − 14.
  1. (x + 7)(x − 2)
  2. (x − 7)(x + 2)
  3. (x − 7)(x − 2)
(b)Factorise 3x² + 10x − 8.
  1. (3x − 4)(x + 2)
  2. (3x + 2)(x − 4)
  3. (3x − 2)(x + 4)
(c)Factorise 4x² − 25y².
  1. (2x − 5y)(2x + 5y)
  2. (4x − 5y)(4x + 5y)
  3. (2x − 5y)²
Show the answers

(a) (x − 7)(x + 2)

(b) (3x − 2)(x + 4)

(c) (2x − 5y)(2x + 5y)

Your turn: Higher Level questions on Factorising.

Higher Level

Asked on 3 of the last 5 Higher Level papers, most recently in 2024. most years

Every paper, year by year

YearWhere it came up
2026Not asked
2025Not asked
2024Q11
2023Q9
2022Q9

Links open the State Examinations Commission’s paper for that year.

Ordinary Level

Asked on 5 of the last 5 Ordinary Level papers, most recently in 2026. banker

Every paper, year by year

YearWhere it came up
2026Q12
2025Q10
2024Q12
2023Q14
2022Q13

Links open the State Examinations Commission’s paper for that year.

More Factorising questions

Factorising, 2 marks

Factorise 6x + 9.

  1. 6(x + 9)
  2. 3(2x + 9)
  3. 3(2x + 3)
Show the answer

3(2x + 3)

The HCF of 6x and 9 is 3. Take it outside: 6x ÷ 3 = 2x and 9 ÷ 3 = 3, giving 3(2x + 3). Expand to check.

Factorising, 3 marks

Factorise x² + 7x + 10.

  1. (x + 3)(x + 4)
  2. (x + 2)(x + 5)
  3. (x + 1)(x + 10)
Show the answer

(x + 2)(x + 5)

Find two numbers that multiply to 10 and add to 7: 2 and 5. So x² + 7x + 10 = (x + 2)(x + 5).

Factorising, 2 marks

Factorise x² + 5x.

  1. x(x + 5)
  2. x(5x + 1)
  3. 5(x² + x)
Show the answer

x(x + 5)

Both terms contain x, so take x outside: x² ÷ x = x and 5x ÷ x = 5. So x(x + 5). Multiply out to check.

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