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Grade 7 · Higher · free GCSE maths worksheet

Factorising quadratics (ax^2 + bx + c)

When a is not 1.

14 original questions, 41 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 2x2 + 7x + 3

2 marks
Show answer
(2x + 1)(x + 3)
2

Factorise 2x2 + 5x − 3

2 marks
Show answer
(2x - 1)(x + 3)
3

Factorise 3x2 - 10x + 8

2 marks
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(3x - 4)(x - 2)
4

Factorise 4x2 − 25

2 marks
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(2x - 5)(2x + 5)
5

Solve 2x2 + 5x - 12 = 0

3 marks
Show answer
x = 32, x = -4
6

Factorise fully 18x2 − 50

3 marks
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2(3x - 5)(3x + 5)
7

Solve 3x2 - 11x + 6 = 0

3 marks
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x = 23, x = 3
8

Solve 3x2 = 5x + 2

3 marks
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x = -1/3 or x = 2
9

Solve 5x2 + 13x - 6 = 0

3 marks
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x = 25, x = -3
10

Simplify fully 2x2 + 5x − 34x2 − 1

3 marks
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(x + 3)/(2x + 1)
11

Factorise 6x2 - 7x - 20

3 marks
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(3x + 4)(2x - 5)
12

The area of a rectangle is (6x2 + 11x − 10) cm2. One side of the rectangle is (3x − 2) cm.

  1. Find an expression, in terms of x, for the length of the other side.

  2. The perimeter of the rectangle is 26 cm. Work out the value of x.

5 marks
Show answer
a) (2x + 5) cm b) 2
13

Solve 6x2 + x - 12 = 0

You must show clear algebraic working.

4 marks
Show answer
x = 43, x = -32
14

Factorise 12x2 + x − 6

3 marks
Show answer
(4x + 3)(3x - 2)

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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