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Factorisation

ICSE · Class 8 · Mathematics

Practice quiz for Factorisation — ICSE Class 8 Mathematics. MCQs and questions with answers to test your preparation.

62 questions24 flashcards5 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·
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Sample Questions

1multiple choice
3 marks

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

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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).

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Frequently Asked Questions

What are the important topics in Factorisation for ICSE Class 8 Mathematics?
Factorisation covers several key topics that are frequently asked in ICSE Class 8 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Factorisation — ICSE Class 8 Mathematics?
Understand the core concepts first, then work through the 62 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

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

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