Factorising Quiz
Test your knowledge of Factorising for GCSE Maths, with this quiz.
This quiz consists of 15 questions, including multiple-choice and short-answer questions on the topic of Factorising for GCSE Maths.
For multiple-choice questions, choose the correct answer. Scroll down to begin the quiz.
Questions
Factorise: x² + 5x + 6
Incorrect
Correct
Incorrect
Incorrect
Factorise: x² − 4
Incorrect
Incorrect
Correct
Incorrect
Factorise: x² + x − 6
Correct
Incorrect
Incorrect
Incorrect
Factorise: 4x² − 9
Incorrect
Incorrect
Incorrect
Correct
Factorise: x² − x − 20
Incorrect
Correct
Incorrect
Incorrect
Factorise: x² - 25
Working:
This is a difference of squares:
$x^2 - 25 = (x - 5)(x + 5)$
Answer: $(x - 5)(x + 5)$
Factorise: 2x² + 7x + 3
Working:
Find two numbers that multiply to 2 × 3 = 6 and add to 7:
6 and 1
Split the middle term:
2x² +6x + x + 3
Group terms:
(2x² + 6x)+(x+3) = 2x(x+3) + 1(x+3)
Factor:
=(2x + 1)(x + 3)
Answer: (2x + 1)(x + 3)
Factorise: 3x² − 12x
Working:
Take out the common factor:
3x(x − 4)
Answer: 3x(x - 4)
Factorise: 4x² −1
Working:
Difference of squares:
4x² − 1 =(2x − 1)(2x + 1)
Answer: (2x - 1)(2x + 1)
Factorise: x² + 2x − 15
Working:
Numbers that multiply to −15 and add to 2:
5 and −3
x² +2x − 15 = (x + 5)(x − 3)
Answer: (x + 5)(x - 3)
Factorise: 6x² − 5x − 6
Working:
Find two numbers that multiply to −36 (i.e., 6 ×−6 and add to −5:
−9 and 4
Split the middle term:
6x² − 9x +4x − 6
Group terms:
(6x² − 9x)+(4x − 6) = 3x(2x − 3) + 2(2x − 3)
Factor:
=(3x + 2)(2x − 3)
Answer: (3x + 2)(2x − 3)
Factorise: x² − x − 12
Working:
Numbers that multiply to −12 and add to −1:
−4 and 3
x² −x − 12= (x − 4)(x + 3)
Answer: (x − 4)(x + 3)
Factorise: 9x² + 6x
Working:
Take out the common factor:
3x(3x + 2)
Answer: 3x(3x + 2)
Factorise: 16x² − 49
Working:
Difference of squares:
(4x − 7)(4x + 7)
Answer: (4x - 7)(4x + 7)
Factorise: 2x² + 9x + 10
Working:
Look for two numbers that multiply to 2 × 10 = 20 and add to 9:
4 and 5
Split the middle term:
2x² +4x +5x + 10
Group:
2x(x + 2) + 5(x + 2)
Factor:
=(2x + 5)(x + 2)
Answer: (2x + 5)(x + 2)
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