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Factorisation Practice Questions

Class 8 · Mathematics · 992 free MCQs with instant results and detailed explanations.

992
Total
321
Easy
509
Medium
162
Hard

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Topics in Factorisation

Division of Expressions 266
Common Factor Method 373
Factors of Algebraic Expressions 353

Sample Questions from Factorisation

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What are the factors of the algebraic expression 3x^2 + 6x?
A. 3x(x + 2)
B. 3(x^2 + 2x)
C. x(3x + 6)
D. 3x^2(1 + 2)
Show Answer & Explanation
Correct Answer: A
The expression 3x^2 + 6x can be factored by taking out the common factor, which is 3x, resulting in 3x(x + 2).
Q2
Easy
What is the factorization of x^2 - 9?
A. (x - 3)(x + 3)
B. (x - 9)(x + 1)
C. (x + 3)(x + 3)
D. (x - 1)(x + 9)
Show Answer & Explanation
Correct Answer: A
The expression x^2 - 9 is a difference of squares and can be factored as (x - 3)(x + 3).
Q3
Easy
Which of the following is a common factor of 12x and 18y?
A. 6
B. 2xy
C. 3y
D. 36xy
Show Answer & Explanation
Correct Answer: A
The greatest common factor of 12 and 18 is 6, which is a common factor of both expressions.
Q4
Medium
What is the factorization of the expression x^2 - 9?
A. (x - 3)(x + 3)
B. (x - 3)^2
C. (x + 3)^2
D. (x + 3)(x - 3)
Show Answer & Explanation
Correct Answer: A
The expression is a difference of squares, which factors into (x - 3)(x + 3).
Q5
Medium
Which of the following is a correct factorization of x^2 + 5x + 6?
A. (x + 2)(x + 3)
B. (x + 1)(x + 6)
C. (x - 2)(x - 3)
D. (x + 3)(x - 2)
Show Answer & Explanation
Correct Answer: A
The expression factors into (x + 2)(x + 3) because 2 and 3 add up to 5 and multiply to 6.
Q6
Medium
Factor the expression 3x^2y - 6xy^2.
A. 3xy(x - 2y)
B. 3x^2y(y - 2x)
C. 3x(y^2 - 2xy)
D. 3xy^2(x - 2y)
Show Answer & Explanation
Correct Answer: A
Factoring 3xy out of the expression gives 3xy(x - 2y).
Q7
Medium
Which expression is equivalent to (x + 1)(x - 1)?
A. x^2 + 1
B. x^2 - 1
C. x^2 + 2
D. x^2 - 2
Show Answer & Explanation
Correct Answer: B
This is a difference of squares and simplifies to x^2 - 1.
Q8
Hard
Which of the following expressions is correctly factored as a product of binomials?
A. x² - 9 = (x - 3)(x + 3)
B. x² + 8x + 16 = (x + 4)(x + 4)
C. x² - 5x + 6 = (x - 2)(x - 3)
D. x² + 7x - 10 = (x + 2)(x - 5)
Show Answer & Explanation
Correct Answer: A
The expression x² - 9 is a difference of squares, factored as (x - 3)(x + 3).
Q9
Hard
What is the greatest common factor (GCF) of the expression 12x²y and 16xy²?
A. 4xy
B. 2xy
C. 8xy
D. 3xy
Show Answer & Explanation
Correct Answer: A
The GCF is found by taking the lowest powers of the common factors: 4 from coefficients and xy from variables.
Q10
Hard
Which of the following represents the factorization of 2x² - 18?
A. 2(x - 3)(x + 3)
B. 2(x + 3)(x - 3)
C. 2(x - 9)(x + 1)
D. 2(x² - 9)
Show Answer & Explanation
Correct Answer: A
The expression is factored as 2 times the difference of squares x² - 9, so (x - 3)(x + 3).

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Factorisation — Class 8 Mathematics Practice Questions Online

This page contains 992 practice MCQs for the chapter Factorisation in Class 8 Mathematics. The questions are organized by difficulty — 321 easy, 509 medium, 162 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.