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Grade 5 · Foundation and Higher · free GCSE maths worksheet

Factorising quadratics (x^2 + bx + c)

Finding two numbers that multiply and add.

14 original questions, 43 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Factorise  x2 - 49

1 mark
Show answer
(x + 7)(x - 7)
2

Factorise x2 + 10x + 21

2 marks
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(x + 3)(x + 7)
3

Factorise x2 − 9x + 20

2 marks
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(x - 4)(x - 5)
4

Factorise  x2 + 9x + 14

2 marks
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(x + 2)(x + 7)
5

Factorise x2 + 5x − 24

2 marks
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(x + 8)(x - 3)
6
  1. Factorise x2 − 3x − 40
  2. Expand and simplify your answer to part a to check it.
3 marks
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a) (x - 8)(x + 5) b) x2 - 3x - 40
7

Simplify fully x2 − 16x + 4

3 marks
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x - 4
8
  1. Expand and simplify  (x + 9)(x - 2)
  2. Factorise  x2 - 3x - 28
4 marks
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a) x2 + 7x - 18 b) (x - 7)(x + 4)
9

By writing 732 − 272 as a product of two factors, work out its value without a calculator.

3 marks
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4600
10

Factorise fully 3x2 − 48

3 marks
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3(x + 4)(x - 4)
11
  1. Expand and simplify (x + 5)(x − 2) + 2(x + 2)
  2. Factorise your answer to part a.
4 marks
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a) x2 + 5x - 6 b) (x + 6)(x - 1)
12
  1. Expand and simplify  (y + 7)(y - 7)
  2. Factorise  x2 + x - 30
4 marks
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a) y2 - 49 b) (x + 6)(x - 5)
13

Amy is asked to factorise x2 - 4x - 12.

She writes  x2 - 4x - 12 = (x - 6)(x - 2)

  1. Explain why Amy's answer is wrong, and write down the correct factorisation.
  2. Factorise fully  2x2 + 6x - 20
5 marks
Show answer
a) (x - 6)(x + 2) b) 2(x + 5)(x - 2)
14
  1. Solve 5 − 2x ≥ 1
  2. Factorise x2 + 5x + 6
5 marks
Show answer
a) x <= 2 b) (x + 2)(x + 3)

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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