Master middle term splitting with these must-practice algebra questions

Welcome to your go-to guide for practicing middle term splitting questions. This method is used in algebra to factorize quadratic expressions by breaking the middle term into two parts. Below, you’ll find 50 carefully selected questions with straightforward answers, explained in a simple way—no formulas, no jargon. Just clean, easy-to-understand solutions that’ll help you master this skill confidently.

Let’s get into it.

Factor the expression: x² + 7x + 12
Answer: (x + 3)(x + 4)

Factor the expression: x² + 5x + 6
Answer: (x + 2)(x + 3)

Factor the expression: x² + 11x + 24
Answer: (x + 3)(x + 8)

Factor the expression: x² + 9x + 20
Answer: (x + 4)(x + 5)

Factor the expression: x² + 10x + 25
Answer: (x + 5)(x + 5)

Factor the expression: x² + 13x + 40
Answer: (x + 5)(x + 8)

Factor the expression: x² + 6x + 9
Answer: (x + 3)(x + 3)

Factor the expression: x² + 15x + 56
Answer: (x + 7)(x + 8)

Factor the expression: x² + 12x + 35
Answer: (x + 5)(x + 7)

Factor the expression: x² + 14x + 49
Answer: (x + 7)(x + 7)

Factor the expression: x² – x – 6
Answer: (x – 3)(x + 2)

Factor the expression: x² + 2x – 8
Answer: (x – 2)(x + 4)

Factor the expression: x² – 5x + 6
Answer: (x – 2)(x – 3)

Factor the expression: x² – 3x – 10
Answer: (x – 5)(x + 2)

Factor the expression: x² – 4x – 21
Answer: (x – 7)(x + 3)

Factor the expression: x² – 6x + 9
Answer: (x – 3)(x – 3)

Factor the expression: x² – 8x + 16
Answer: (x – 4)(x – 4)

Factor the expression: x² – 10x + 25
Answer: (x – 5)(x – 5)

Factor the expression: x² – 12x + 35
Answer: (x – 5)(x – 7)

Factor the expression: x² – 14x + 45
Answer: (x – 5)(x – 9)

Factor the expression: x² + x – 12
Answer: (x + 4)(x – 3)

Factor the expression: x² + 3x – 18
Answer: (x + 6)(x – 3)

Factor the expression: x² – x – 20
Answer: (x – 5)(x + 4)

Factor the expression: x² – 9x + 18
Answer: (x – 6)(x – 3)

Factor the expression: x² + 4x – 21
Answer: (x + 7)(x – 3)

Factor the expression: x² – 7x + 10
Answer: (x – 5)(x – 2)

Factor the expression: x² + 6x – 16
Answer: (x + 8)(x – 2)

Factor the expression: x² – 3x – 28
Answer: (x – 7)(x + 4)

Factor the expression: x² – 11x + 30
Answer: (x – 5)(x – 6)

Factor the expression: x² + 8x – 9
Answer: (x + 9)(x – 1)

Factor the expression: x² – 13x + 36
Answer: (x – 9)(x – 4)

Factor the expression: x² + 10x – 24
Answer: (x + 12)(x – 2)

Factor the expression: x² + 2x – 35
Answer: (x + 7)(x – 5)

Factor the expression: x² – 15x + 50
Answer: (x – 10)(x – 5)

Factor the expression: x² + 9x – 10
Answer: (x + 10)(x – 1)

Factor the expression: x² – 2x – 15
Answer: (x – 5)(x + 3)

Factor the expression: x² + x – 42
Answer: (x + 7)(x – 6)

Factor the expression: x² + 13x + 30
Answer: (x + 10)(x + 3)

Factor the expression: x² + 14x + 45
Answer: (x + 9)(x + 5)

Factor the expression: x² + 7x – 44
Answer: (x + 11)(x – 4)

Factor the expression: x² – 6x – 55
Answer: (x – 11)(x + 5)

Factor the expression: x² – 2x – 24
Answer: (x – 6)(x + 4)

Factor the expression: x² + 5x – 50
Answer: (x + 10)(x – 5)

Factor the expression: x² – 9x – 22
Answer: (x – 11)(x + 2)

Factor the expression: x² – 5x – 14
Answer: (x – 7)(x + 2)

Factor the expression: x² + 4x – 60
Answer: (x + 10)(x – 6)

Factor the expression: x² + x – 56
Answer: (x + 8)(x – 7)

Factor the expression: x² + 12x – 64
Answer: (x + 16)(x – 4)

Factor the expression: x² – 4x – 60
Answer: (x – 10)(x + 6)

Factor the expression: x² – x – 72
Answer: (x – 9)(x + 8)

Top Indian Books for Practicing Middle Term Splitting Questions with Authors and Publishers

1. Mathematics for Class 9 by R.D. Sharma – Dhanpat Rai Publications
   Includes extensive exercises on middle term splitting under factorization. Step-by-step questions progress from simple to challenging, suitable for school exams.

2. Secondary School Mathematics for Class 10 by R.S. Aggarwal – Bharti Bhawan Publishers
   Contains practice sets on quadratic expressions with a separate section focusing on middle term splitting in factorization chapters.

3. Foundation Mathematics for Class 9 by M.L. Aggarwal – Arya Publications
   Offers conceptual clarity with solved and unsolved questions. Middle term splitting is explained with logical reasoning and followed by graded exercises.

4. ICSE Mathematics Class 9 by Anindita Roy – Selina Publishers
   Designed for ICSE board students, this book breaks down algebraic factorization using intuitive examples and varied middle term splitting problems.

5. Understanding ICSE Mathematics Class 10 by M.L. Aggarwal – Avichal Publishing Company
   Covers all aspects of algebra including advanced middle term splitting questions. Exercises are board-exam oriented.

6. Mathematics Today Class 9 by S.K. Gupta & Anubhuti Gangal – S. Chand Publications
   Focuses on conceptual development with topic-wise exercises. Factorization using middle term splitting is covered with MCQs and HOTS questions.

7. Skills in Mathematics – Algebra for JEE Main & Advanced by Arihant Experts – Arihant Publications
   For competitive aspirants, it has application-based and analytical middle term splitting questions. Stepwise approaches are highlighted for deeper understanding.

8. Self-Study Guide: Mathematics Class 10 by Arihant Experts – Arihant Publications
   A comprehensive guide with topic tests, solved board papers, and smart tricks for solving middle term splitting questions efficiently.

9. Mathematics Class 10 by S. K. Jain – VK Global Publications
   Offers conceptual and practice-based middle term splitting problems. Ideal for quick revision with test-yourself sections after each topic.

10. Exemplar Problems: Mathematics Class 9 by NCERT – NCERT Publications
    Focuses on logical reasoning and problem-solving. Includes middle term splitting in the algebraic expression section with short and long questions.

11. Target Mathematics Class 10 by S.K. Singh – Cordova Publications
    A perfect blend of theory and practice with exam-style middle term splitting questions. Also includes practice worksheets.

12. All-in-One Mathematics CBSE Class 9 by Arihant Experts – Arihant Publications
    A self-study book that breaks down algebraic concepts with real-life applications. Middle term splitting questions follow each concept explanation.

13. Basic Mathematics for Class 9 by L.K. Sharma – Evergreen Publications
    Provides fundamental understanding with examples and quick concept checks. Factorization is practiced through detailed middle term splitting questions.

14. CBSE Chapterwise Mathematics Class 10 by Oswal – Oswal Publishers
    A chapter-by-chapter breakdown with board questions. Middle term splitting is tested through multiple solved and unsolved board-style problems.

15. CBSE Mathematics Class 10 Standard by U-Like – Best Book Publishing Co. Pvt. Ltd.
    Practice-focused book offering model test papers and chapter-wise exercises. Includes typical and tricky middle term splitting questions.

16. Mathematics Practice Book Class 9 by R.K. Bansal – Full Marks Pvt. Ltd.
    Focuses on building problem-solving skills. Includes application-level middle term splitting questions with detailed hints.

17. Xam Idea Mathematics Class 10 by VK Global – VK Global Publications
    Good for revision and practice. Includes board pattern questions and concept maps, with focused sections on middle term splitting methods.

18. New Learning Mathematics Class 9 by M. L. Aggarwal – Avichal Publishing Company
    Detailed explanation of middle term splitting techniques followed by a range of basic and advanced problems.

19. CBSE Success Series Mathematics Class 10 by Dinesh – Dinesh Publications
    Designed for smart preparation, this book includes level-based practice on middle term splitting and other factorization techniques.

20. Step-by-Step Mathematics Class 9 by K.R. Chawla – Evergreen Publications
    Beginner-friendly book with visual approaches and examples for middle term splitting. Ideal for building confidence in algebra.

Mastering Middle Term Splitting Questions for Better Algebra Skills

Middle term splitting questions are a key part of mastering algebra, especially when it comes to factorizing quadratic equations. Whether you’re preparing for school exams, board assessments, or competitive tests, understanding this concept helps build a strong mathematical foundation. It’s one of the most reliable techniques to break down complex expressions and solve them with clarity and confidence.

At its core, middle term splitting is used to factorize a quadratic expression of the form ax² + bx + c. The idea is to split the middle term (the term with ‘x’) into two terms whose coefficients multiply to give the product of the first and the last term. This technique simplifies the process and removes guesswork, making it easier to arrive at the correct factors.

Many students initially struggle with identifying the right pair of numbers that fulfill the condition. That’s why consistent practice is essential. Start with basic problems where the leading coefficient ‘a’ is 1. For example, in the expression x² + 7x + 12, the middle term 7x can be split into 3x and 4x because 3 and 4 multiply to give 12 and add up to 7. The equation then becomes easier to factor: (x + 3)(x + 4).

As students get comfortable, they can move on to problems where ‘a’ is greater than 1. These require a sharper eye and stronger multiplication skills. For instance, with 2x² + 7x + 3, the product of 2 and 3 is 6. The middle term 7x can be split into 6x and 1x, making the factorization 2x² + 6x + x + 3, which becomes (2x + 3)(x + 1) after grouping.

One of the best strategies for mastering middle term splitting is categorizing questions based on difficulty. Begin with expressions that have small, positive integers. Then practice with negative numbers and more complex coefficients. As you progress, include real-world word problems that translate into algebraic equations requiring middle term splitting. This not only enhances comprehension but also boosts confidence.

Use worksheets, mock tests, and previous year papers to challenge your skills. Look for questions that introduce new patterns, such as prime numbers or decimals, to stretch your thinking. Regular revision of common factor pairs also sharpens mental math, which is crucial for time-bound tests.

Teachers and experts recommend solving at least 5–10 questions daily when preparing for exams. Keep a separate notebook to note down difficult problems and review your mistakes. Analyzing where you went wrong—was it the wrong pair of numbers, or did you forget to factor correctly?—can help you avoid repeating the same errors.

To build lasting understanding, explain each step aloud as you solve. This habit strengthens reasoning and uncovers gaps in logic. Peer discussions and group problem-solving sessions can also add variety to your preparation routine.

Middle term splitting questions don’t just test memory; they build reasoning and analytical skills. The more you engage with them, the more intuitive they become. Stay consistent, review often, and don’t be afraid to experiment with different approaches until you find what works best for you.

FAQ for Middle Term Splitting Questions

What is middle term splitting in algebra?
Middle term splitting is a method used to factor quadratic expressions by breaking the middle term into two parts. These parts must add up to the original middle term and multiply to give the product of the first and last coefficients in the expression.

Why is middle term splitting important?
It helps in simplifying quadratic expressions and solving quadratic equations quickly. This method is widely used in school-level math, board exams, and competitive entrance tests.

What type of expressions can be solved using middle term splitting?
Only quadratic expressions of the form ax² + bx + c can be solved using this method. The key is that the expression must be factorable using integers.

Can middle term splitting be used when the coefficient of x² is not 1?
Yes, it works even when the coefficient of x² (denoted as ‘a’) is not 1. You need to multiply ‘a’ and ‘c’, then find two numbers that add to ‘b’ and multiply to the product of ‘a × c’.

What should I do if I can’t find the right pair of numbers to split the middle term?
Try listing all possible factor pairs of the product of ‘a × c’ and then check which pair adds up to ‘b’. Practice improves speed and accuracy in spotting the correct pair.

Are there any shortcuts for middle term splitting?
There’s no shortcut that replaces the logic, but knowing common factor pairs and practicing regularly can make the process much faster.

How is middle term splitting different from other factorization methods?
Unlike methods like completing the square or using the quadratic formula, middle term splitting relies on finding two numbers that satisfy specific multiplication and addition conditions. It’s faster and more intuitive when applicable.

Is middle term splitting included in competitive exams?
Yes, it is frequently asked in exams like NTSE, Olympiads, JEE Foundation, and other school-level or entrance-level competitive tests.

Can negative numbers be used in middle term splitting?
Yes, the numbers used to split the middle term can be positive or negative depending on the sign of the original terms in the quadratic expression.

What is the most common mistake students make in middle term splitting?
Many students pick a pair that multiplies correctly but does not add up to the middle term. It’s essential to check both conditions: multiplication and addition.

How can I improve my skills in middle term splitting?
Practice a variety of questions, starting from basic to advanced. Use worksheets, track mistakes, and regularly review factor pairs for common numbers.

Can middle term splitting be used for all quadratic equations?
No, only for those that can be factored over integers. If no such pair exists, other methods like the quadratic formula may be needed.

Is it necessary to learn middle term splitting?
Yes, especially for students in classes 8 to 10 and those appearing for exams where algebra plays a key role. It builds a solid base in factorization techniques.