Factorisation — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 112
Pre-2026 syllabusThis chapter is from the older NCERT book. See the 2026-27 Class 8 Mathematics chapters →
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 112, "Factorisation". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams apart.
To score well in "Factorisation", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Factorisation, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Factorisation (Class 8 Mathematics)
This chapter covers factorising algebraic expressions by common factors, grouping, identities, and dividing one algebraic expression by another.
- Factorisation
- Writing an expression as a product of its factors — the reverse of expansion.
- Common factor method
- Take out the highest common factor of all terms, e.g. 6x + 9 = 3(2x + 3).
- Regrouping terms
- Rearrange and group terms so each group has a common factor, then factor again.
- Using identities
- Recognise a² ± 2ab + b² and a² − b² to factorise directly.
Factorisation — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 58 are timed and scored when you sign in.
- Q1Easy
Factorise 6x + 9:
A.9(x + 6)B.6(x + 9)C.x(6 + 9)D.3(2x + 3)✓ CorrectAnswer: D. 3(2x + 3)
Explanation: GCD = 3.
- Q2Easy
Factorise x² − 9:
A.(x−3)²B.(x−9)(x+1)C.(x−3)(x+3)✓ CorrectD.(x+3)²Answer: C. (x−3)(x+3)
Explanation: Difference of squares.
- Q3Easy
Factorise 12a + 18:
A.6(2a + 3)✓ CorrectB.3(4a + 9)C.2(6a + 18)D.6(2a + 18)Answer: A. 6(2a + 3)
Explanation: The HCF of 12 and 18 is 6, giving 6(2a + 3).
- Q4Easy
Factorise a² − 1:
A.(a − 1)²B.(a − 1)(a + 1)✓ CorrectC.(a + 1)²D.a(a − 1)Answer: B. (a − 1)(a + 1)
Explanation: This is a² − 1², a difference of two squares.
- Q5Easy
Factorise 7x² + 14x:
A.7(x² + 2x)B.7x(x + 2)✓ CorrectC.x(7x + 14)D.7x(x + 14)Answer: B. 7x(x + 2)
Explanation: The common factor 7x is taken out to give 7x(x + 2).
- Q6Easy
Factorise 25 − y²:
A.(5 − y)(5 + y)✓ CorrectB.(5 − y)²C.(y − 5)(y + 5)D.(5 + y)²Answer: A. (5 − y)(5 + y)
Explanation: This is 5² − y², which factors as (5 − y)(5 + y).
- Q7Medium
Factorise ax + ay + bx + by:
A.(a−b)(x−y)B.(a+b)(x+y)✓ CorrectC.(ax+by)D.(a+x)(b+y)Answer: B. (a+b)(x+y)
Explanation: Group: a(x+y) + b(x+y).
- Q8Medium
Factorise x² + 6x + 9:
A.(x+3)²✓ CorrectB.(x−3)²C.(x+9)(x−1)D.(x+6)²Answer: A. (x+3)²
Explanation: Perfect square.
- Q9Medium
Factorise 6ab − 4a + 9b − 6 by regrouping:
A.(3b + 2)(2a − 3)B.(2a − 3)(3b + 2)C.(3b − 2)(2a + 3)✓ CorrectD.(2a + 3)(3b + 2)Answer: C. (3b − 2)(2a + 3)
Explanation: Group as 2a(3b − 2) + 3(3b − 2) = (3b − 2)(2a + 3).
- Q10Medium
Factorise 49x² − 81y²:
A.(7x + 9y)²B.(7x − 9y)²C.(7x − 9y)(7x + 9y)✓ CorrectD.(49x − 81y)(x + y)Answer: C. (7x − 9y)(7x + 9y)
Explanation: This is (7x)² − (9y)², a difference of squares.
- Q11Medium
Factorise pq − pr + qx − rx by regrouping:
A.(q − r)(p − x)B.(p − x)(q + r)C.(p + x)(q + r)D.(p + x)(q − r)✓ CorrectAnswer: D. (p + x)(q − r)
Explanation: Group as p(q − r) + x(q − r) = (q − r)(p + x).
- Q12Hard
Divide: (12x³ − 8x² + 4x) ÷ 4x:
A.3x³ − 2x² + xB.3x² − 2xC.3x² − 2x + 1✓ CorrectD.3x² − 2x + 4Answer: C. 3x² − 2x + 1
Explanation: Divide each term by 4x: 3x² − 2x + 1.
- Q13Hard
Factorise x² + 5x + 6:
A.(x+5)(x+1)B.(x+1)(x+6)C.(x−2)(x−3)D.(x+2)(x+3)✓ CorrectAnswer: D. (x+2)(x+3)
Explanation: Two numbers: 2,3 (sum 5, product 6).
- Q14Hard
Divide: (x² + 7x + 12) ÷ (x + 3):
A.x + 12B.x + 4✓ CorrectC.x + 3D.x − 4Answer: B. x + 4
Explanation: x² + 7x + 12 = (x + 3)(x + 4), so dividing by (x + 3) leaves x + 4.
Start this chapter free
You have 14 solved above. Sign in with Google (no card needed). You get 1 Easy + 1 Medium quiz on every chapter during your 30-day trial. After that, you keep 1 Easy quiz on every chapter, free for good, plus the full key-concept notes, formulas & exam tips.
This chapter has 72 questions (24 Easy · 24 Medium · 24 Hard), with timed scoring and instant feedback. The rest unlock with the ₹999/year plan.
Start this chapter free →Factorisation — FAQs
What are the key concepts in Class 8 Mathematics Factorisation?+
This chapter covers factorising algebraic expressions by common factors, grouping, identities, and dividing one algebraic expression by another. Key ideas include Factorisation, Common factor method, Regrouping terms, Using identities.
What does Class 8 Mathematics Chapter 112 (Factorisation) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "Factorisation": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams.
Are these "Factorisation" questions free to practise?+
Yes. Sign in with Google to practise "Factorisation" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Factorisation" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Factorisation" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Factorisation" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Factorisation (Class 8 Mathematics)?+
The questions that matter most test Factorisation, Common factor method, Regrouping terms, Using identities. This page shows 14 solved important MCQs with answers and explanations; all 72 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Factorisation?+
Yes — Class 8 Mathematics Factorisation has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.