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Factorisation — Practice Quiz

ICSE · Class 8 · Mathematics

Try a 4-question quiz on Factorisation for ICSE Class 8 Mathematics: tap an answer to check it and see why. 62 questions in the full chapter test.

62 questions24 flashcards4 formulas & key relations5 concepts

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Quick Quiz: Factorisation

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1

Factorise the expression 6x^2 + 11x + 3 by splitting the middle term.

2

Factorise completely 16x^4 - y^4.

3

Factorise 9(x + y)^2 - 16(x - 3y)^2 completely.

4

Factorise x^2 + 4xy + 4y^2 - 9z^2 completely.

62 Questions·
multiple choicemultiple correcttrue false

Sample Questions

1multiple choice
3 marks

Factorise 8x^3 - 18xy^2 completely.

Show answer

2x(2x + 3y)(2x - 3y)

First take out the common factor 2x: 8x^3 - 18xy^2 = 2x(4x^2 - 9y^2). Then use difference of squares: 4x^2 - 9y^2 = (2x + 3y)(2x - 3y). So the complete factorisation is 2x(2x + 3y)(2x - 3y).

2multiple choice
3 marks

Factorise 3x^2 + 12x - 36 completely.

Show answer

3(x + 6)(x - 2)

First take out the common factor 3: 3x^2 + 12x - 36 = 3(x^2 + 4x - 12). Now split 4x into 6x - 2x, since 6 + (-2) = 4 and 6 × (-2) = -12. So x^2 + 4x - 12 = x^2 + 6x - 2x - 12 = x(x + 6) - 2(x + 6) = (x + 6)(x - 2). Therefore the answer is 3(x + 6)(x - 2).

3multiple choice
3 marks

Factorise 1 - 4(a - 2b)^2 completely.

Show answer

(1 + 2a - 4b)(1 - 2a + 4b)

Write 4(a - 2b)^2 as [2(a - 2b)]^2 = (2a - 4b)^2. Then 1 - (2a - 4b)^2 is a difference of squares. So it factorises to (1 + 2a - 4b)(1 - 2a + 4b).

4multiple choice
2 marks

Factorise x^2 - 9x + 20 completely.

Show answer

(x - 5)(x - 4)

Find two numbers whose product is 20 and sum is -9. They are -5 and -4. So x^2 - 9x + 20 = x^2 - 5x - 4x + 20 = x(x - 5) - 4(x - 5) = (x - 5)(x - 4).

+58 more questions on Factorisation (ICSE Class 8 Mathematics)

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Frequently Asked Questions

What are the important topics in Factorisation for ICSE Class 8 Mathematics?
Key topics in Factorisation include Basic Ideas and Common Factors, Factorisation by Grouping, Difference of Two Squares, Factorising Trinomials. Study these first, then practise questions on each for Class 8 exams.
How many practice questions are there for Factorisation?
There are 62 questions on Factorisation. Try the 4-question sample quiz on this page first; each answer shows an explanation when you tap it.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All ICSE Class 8 Mathematics Practice Quiz

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