Class 10 Maths Chapter 2: Polynomials is one of the most important chapters in the CBSE curriculum, carrying a weightage of around 5 marks in the board examination. This chapter focuses on the concepts of zeros of a polynomial, relationships between zeros and coefficients, and the geometrical meaning of zeros. However, the topic “2.4 Division Algorithm for Polynomials” has been deleted from the CBSE Class 10 Maths syllabus (2025–26).
In this article, we bring you the most important and repeated questions from the Polynomials chapter, including 1-mark, 2-mark, 3-mark, and 4-mark case study questions, based on the latest pattern and previous year trends. These questions are carefully curated from previous year question papers and insights from subject matter experts.
Practising these questions will help students score full marks in this chapter and strengthen their understanding of polynomial identities, quadratic equations, and graphical interpretation of zeros.
CBSE Class 10 Maths Exam 2026: Key Highlights
| Particulars | Details |
| Board | Central Board of Secondary Examination (CBSE) |
| Exam Mode | Offline |
| Subject | Mathematics |
| Paper Name | Maths Standard and Maths Basic |
| Chapter Name | Polynomials |
| Chapter Weightage | 5 Marks (Both Standard and Basic) |
| Medium/ Language | English and Hindi |
| Exam Duration | 3 Hours |
| Total Marks | 100 |
| Theory Paper | 80 Marks |
| Internal Assessment | 20 Marks |
| CHECK: CBSE Class 10 Maths Chapter 1 Real Number Important Questions with Answers |
Important Questions and Answers for CBSE Class 10 Maths Chapter 2: Polynomials
SECTION A: ONE MARKS
SECTION B: TWO MARKS
SECTION C: THREE MARKS
SECTION D: FOUR MARKS (CASE STUDY BASED)
Case Study 1:
A parabolic bridge has an arch represented by the equation y=−x2+4xy = -x^2 + 4xy=−x2+4x.
Answer the following:
(i) At what points does the arch touch the ground?
(ii) Identify the polynomial and its degree.
(iii) Find its zeros and interpret them.
(iv) Draw a rough sketch of the parabola.
Case Study 2:
A gardener designs a flowerbed in a parabolic shape given by p(x)=x2−5x+6.
Answer the following:
(i) Find the zeros of the polynomial.
(ii) What do these zeros represent in the design?
(iii) Verify the relationship between zeros and coefficients.
(iv) If the width of the garden is equal to the difference between zeros, find the width.
Case Study 3:
The path of a ball thrown upward is given by h(x)=−5x2+20x+15 is the height.
(i) Find the time when the ball hits the ground (i.e. when h=0).
(ii) Find the maximum height.
(iii) Identify the type and degree of the polynomial.
(iv) Interpret the zeros in the context of time.
Case Study 4:
A company’s profit (in ₹ thousand) is given by P(x)=−x2+6x−5, where x is the number of items sold.
(i) Find the number of items for which the company makes no profit.
(ii) Find the maximum profit.
(iii) What do the zeros signify here?
(iv) Find the value of x for which profit is maximum.
| CHECK: CBSE Class 10 Maths Chapter 5 Arithmetic Progressions Important Questions with Answers |
Answers:
SECTION A
| Question No. | Answer |
| 1. | k=−4 |
| 2. | k=−3/2 |
| 3. | Sum of zeros = −b/a, Product of zeros = c/a |
| 4. | x=2 |
| 5. | x=0,2 |
| 6. | x2−5x+6 |
| 7. | Sum of zeros = –4 |
| 8. | 0 real zeros |
| 9. | 0 |
| 10. | a=4 |
SECTION B
| Question No. | Answer |
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| |
SECTION C
| Question No. | Answer |
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SECTION D
| Question No. | Answer |
| 1. |
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| 2. |
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| 3. |
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| 4. |
(iii) The zeros represent the number of items for which the company’s profit is zero, i.e., no profit or loss points. (iv) The profit is maximum when 3 items are sold. |
To Check all the detailed answers of the important question of CBSE Class 10 Maths Chapter 2: Polynomials, Download PDF from the link provided below:
CBSE Class 10 Maths Chapter 2 Polynomials: Download PDF of Important Questions and Answers |
CBSE Class 10 Maths: Deleted Syllabus 2026
The deleted section for Chapter 2: Polynomials in the CBSE Class 10 Maths syllabus for the 2025-2026 Board Examination is the "Division algorithm for polynomials".
This means students are not required to study the Statement and simple problems on the division algorithm for polynomials with real coefficients. Specifically, the content and exercises related to the long division of polynomials found on pages 33-37 (Section 2.4: Division algorithm for polynomials) in the old NCERT textbook have been removed from the curriculum and will not be assessed in the board exams.
These deletions aim to focus on core concepts and facilitate a more manageable study plan. For a comprehensive list of all deleted topics across subjects, please refer to the full article below:
| Related: CBSE Class 10 Deleted Syllabus 2025–26: Subject-wise List of Removed Topics |
CBSE Class 10 Maths Board Exams requires focused practice on high-yield questions from all chapters. To streamline your revision and ensure you cover only the most important questions guaranteed to boost your confidence, you can instantly access the complete, chapter-wise compilation specifically designed for dedicated board students simply click the below link to get the important questions of CBSE Class 10 maths of all chapters from here for board students.
CHECK: CBSE Class 10 Maths Important Questions with Answers 2026: All Subjects |
Mastering Class 10 Maths Chapter 2: Polynomials is essential for scoring well in the CBSE board exams. This chapter builds the foundation for algebraic concepts in higher classes and frequently appears in exams with both direct and application-based questions. By practising these important and repeated questions of 1, 2, 3, and 4 marks, students can improve accuracy and boost confidence. Remember, the topic “Division Algorithm for Polynomials” has been removed from the syllabus (2025–26), so focus on the remaining key concepts, zeros, relationships between coefficients, and graphical understanding. Consistent practice of these questions ensures full marks in this 5-mark chapter in the Class 10 Board Exam 2025.
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