How many practice questions are available for Factorization?

SparkEd Math offers 60+ practice questions for Factorization across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Factorization content free on SparkEd Math?

Yes! All Factorization content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Factorization differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Factorization problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Factorization content aligned with the CBSE syllabus?

Yes, all Factorization questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Factorization — Class 8 CBSE (2025-26)

About Factorization — Class 8 CBSE

Factorize algebraic expressions using common factors, regrouping, and identities. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 13). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Factorization

Introduction to Factorization: Breaking Down Expressions
Factorization by Common Factors: The HCF Method
Factorization by Grouping: When Terms Don't Share Everything
Factorization Using Algebraic Identities: Smart Shortcuts
Summary and Practice: Mastering Factorization

Interactive lesson · about 15 minutes · checkpoint question after every unit

Factorization — solved examples for Class 8 CBSE

Example 1easy

Which of the following statements best describes the process of factorization of an algebraic expression?

A)It is the process of multiplying two or more algebraic expressions to get a single expression.
B)It is the process of breaking down an algebraic expression into a product of two or more simpler expressions (its factors).
C)It is the process of finding the value of a variable in an algebraic expression.
D)It is the process of adding or subtracting like terms in an algebraic expression.

Step-by-step solution

Factorization is essentially the reverse process of multiplication.
When we factorize an algebraic expression, we express it as a product of two or more simpler expressions, which are called its factors.

Answer: It is the process of breaking down an algebraic expression into a product of two or more simpler expressions (its factors).

Example 2medium

Factorize the algebraic expression: 12a³b + 18a²b² - 24ab³

A)6ab(2a² + 3ab - 4b²)
B)6a²b(2a + 3b - 4b²)
C)6ab(2a² + 3ab - 4b)
D)6ab(2a² + 3ab - 4b³)

Step-by-step solution

Identify the GCF of the numerical coefficients (12, 18, 24). The GCF is 6.
Identify the GCF of the variable parts (a³b, a²b², ab³). The lowest power of 'a' is a¹, and the lowest power of 'b' is b¹. So, the GCF is ab.
Combine these to get the overall GCF: 6ab.
Divide each term by the GCF: (12a³b / 6ab) + (18a²b² / 6ab) - (24ab³ / 6ab) = 2a² + 3ab - 4b². Therefore, the factored expression is 6ab(2a² + 3ab - 4b²).

Answer: 6ab(2a² + 3ab - 4b²)

Example 3hard

Factorize completely: 3x²y(a - 2b)² - 9xy²(a - 2b)

A)3xy(a - 2b)[x(a - 2b) - 3y]
B)3xy(a - 2b)[x(a - 2b) + 3y]
C)3xy(a - 2b)[3y - x(a - 2b)]
D)3xy(a - 2b)[x(2b - a) - 3y]

Step-by-step solution

Identify the common numerical factor, common variable factors, and common binomial factor. The common numerical factor is 3, common variable factors are x and y, and the common binomial factor is (a - 2b).
Factor out 3xy(a - 2b) from both terms.
$3x²y(a - 2b)² - 9xy²(a - 2b) = 3xy(a - 2b)[x(a - 2b) - 3y]$
The first term becomes x(a - 2b) and the second term becomes -3y after factoring out the common expression.

Answer: 3xy(a - 2b)[x(a - 2b) - 3y]

Practice questions on Factorization

Q1.easy
Factorize the expression 6xy - 9x.
1. A)3x(2y - 3x)
2. B)3x(2y - 3)
3. C)3(2xy - 3x)
4. D)3x(2y + 3)
Show answer
Answer: 3x(2y - 3)
Hint: Look for the greatest common factor (GCF) of the numerical coefficients and the variables in both terms.
Q2.easy
Rahul factorized the expression 12a²b + 18ab² as follows:
Step 1: Found the greatest common factor (GCF) of 12a²b and 18ab² as 6ab.
Step 2: Divided each term by the GCF: (12a²b) ÷ (6ab) = 2a and (18ab²) ÷ (6ab) = 3b.
Step 3: Wrote the factored form as 6ab(2a + 3b).
Which of the following statements is true regarding Rahul's solution?
1. A)Step 1 is incorrect because the GCF should be 3ab.
2. B)Step 2 is incorrect because (18ab²) ÷ (6ab) should be 3ab.
3. C)Step 3 is incorrect because the terms inside the bracket should be subtracted.
4. D)Rahul's solution is completely correct.
Show answer
Answer: Rahul's solution is completely correct.
Hint: Carefully re-evaluate each step. Check the GCF, then the division of each term, and finally the final factored form.
Q3.easy
Factorize the expression ab + bc + ax + cx.
1. A)(a + c)(b + x)
2. B)(a + b)(c + x)
3. C)(a + x)(b + c)
4. D)(a + c)(b - x)
Show answer
Answer: (a + x)(b + c)
Hint: Group terms that share common factors, then factor out the common binomial expression.
Q4.medium
Which of the following expressions has (5x - 2) as a factor?
1. A)10x² + 4x - 5
2. B)15x² - 6x - 10x + 4
3. C)25x² - 4
4. D)5x² - 7x + 2
Show answer
Answer: 15x² - 6x - 10x + 4
Hint: Try to factorize each option or substitute x = 2/5 into the expressions to see which one becomes zero.
Q5.medium
Factorize by grouping: ax - ay - bx + by
1. A)(a - b)(x - y)
2. B)(a + b)(x - y)
3. C)(a - b)(x + y)
4. D)(a + b)(x + y)
Show answer
Answer: (a - b)(x - y)
Hint: Group the terms in pairs and factor out common factors from each pair. Pay close attention to the signs.
Q6.medium
Rhea was asked to factorize 7x² - 14xy - 5x + 10y. She wrote:
Step 1: 7x(x - 2y) - 5(x - 2y)
Step 2: (x - 2y)(7x - 5)
What mistake, if any, did Rhea make in her factorization?
1. A)There is no mistake; the factorization is correct.
2. B)In Step 1, the sign of the second term should be +5(x - 2y).
3. C)In Step 1, the terms were grouped incorrectly.
4. D)The expression cannot be factorized by grouping.
Show answer
Answer: There is no mistake; the factorization is correct.
Hint: Carefully check each step. When factoring out a negative number, remember to change the signs of the terms inside the parenthesis.
Q7.hard
Factorize the expression: x² - 2xy + y² - 4z²
1. A)(x - y - 2z)(x - y + 2z)
2. B)(x + y - 2z)(x - y + 2z)
3. C)(x - y - 2z)(x + y + 2z)
4. D)(x - y)² - (2z)²
Show answer
Answer: (x - y - 2z)(x - y + 2z)
Hint: Look for a perfect square trinomial first, and then apply the difference of squares identity.
Q8.hard
If x + 1/x = 5, then the value of x² + 1/x² is:
1. A)23
2. B)25
3. C)27
4. D)5
Show answer
Answer: 23
Hint: Consider squaring the given equation and see how it relates to the expression you need to find.
Q9.hard
Ravi was asked to factorize 9a² - 16b² + 3a + 4b. He wrote the solution as (3a - 4b)(3a + 4b) + (3a + 4b). What mistake did Ravi make, if any, in the final factorization step?
1. A)There is no mistake; the factorization is complete.
2. B)He did not factor out the common binomial (3a + 4b).
3. C)He incorrectly applied the difference of squares identity.
4. D)He should have regrouped the terms differently at the beginning.
Show answer
Answer: He did not factor out the common binomial (3a + 4b).
Hint: After applying the difference of squares, look for any common factors that can be further extracted from the entire expression.

These are 9 of the 60 questions available for Factorization. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.