Chapter 2 · Class 10 CBSE · Free Worksheet PDF

Polynomial Sums for Class 10 — Free CBSE Worksheet PDF with Answers

Download a free printable polynomials worksheet for Class 10 CBSE with 30 practice questions covering polynomials, degree, zeroes, factor theorem, remainder theorem, and factorisation of polynomials. Includes complete answer key. CBSE-aligned for the 2025-26 syllabus.

Last updated: 5 May 2026

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30 questions (Easy + Medium + Hard) with answer key. Fresh set generated daily.

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Sample Polynomials Sums for Class 10 — Practice Questions

Here are 8 sample polynomials sums from this Class 10 CBSE worksheet. Download the full PDF for all 30 questions with answers.

Q1.If 'k' is a zero of the polynomial P(x) = ax² + bx + c, which of the following statements must be true?
A.P(k) = 0
B.P(0) = k
C.P(k) = c
D.P(x) = k

Difficulty: Easy

Q2.Which of the following expressions represents a quadratic polynomial?
A.2x + 5
B.3x² - 4x + 1
C.x³ + 2x - 7
D.4x⁴

Difficulty: Easy

Q3.A graph of a polynomial y = P(x) is shown. If this graph intersects the x-axis at exactly three distinct points, say at x = -2, x = 1, and x = 3, what can be concluded about the number of zeros of P(x)?
A.P(x) has no real zeros.
B.P(x) has exactly two real zeros.
C.P(x) has exactly three real zeros.
D.P(x) must be a quadratic polynomial.

Difficulty: Easy

Q4.Ravi was finding the sum of zeros for the quadratic polynomial x² - 7x + 10. He stated that the sum of zeros is 7. Is his calculation correct? If not, what is the correct sum?
A.Yes, the sum is 7.
B.No, the sum is -7.
C.No, the sum is 10.
D.Yes, the sum is 7 because -(-7)/1 = 7.

Difficulty: Easy

Q5.If the sum of the zeros of a quadratic polynomial is -5 and the product of its zeros is 6, which of the following could be the polynomial?
A.x² + 5x + 6
B.x² - 5x + 6
C.x² + 5x - 6
D.x² - 5x - 6

Difficulty: Easy

Q6.According to the Division Algorithm for polynomials, if P(x) is divided by G(x) (where G(x) ≠ 0), resulting in quotient Q(x) and remainder R(x), which of the following statements about the degree of the remainder R(x) is always true?
A.Degree of R(x) > Degree of G(x)
B.Degree of R(x) < Degree of G(x) or R(x) = 0
C.Degree of R(x) = Degree of G(x)
D.Degree of R(x) is always 0

Difficulty: Easy

Q7.Which of the following quadratic polynomials has zeros 2 and -3?
A.x² + x + 6
B.x² - x - 6
C.x² + x - 6
D.x² - 5x + 6

Difficulty: Easy

Q8.If α and β are the zeros of the quadratic polynomial P(x) = ax² + bx + c, then what is the value of 1/α + 1/β?
A.c/a
B.-b/a
C.b/c
D.-b/c

Difficulty: Easy

Answer Key — Sample Questions+
Q1:P(k) = 0
Q2:3x² - 4x + 1
Q3:P(x) has exactly three real zeros.
Q4:Yes, the sum is 7 because -(-7)/1 = 7.
Q5:x² + 5x + 6
Q6:Degree of R(x) < Degree of G(x) or R(x) = 0
Q7:x² + x - 6
Q8:-b/c

Download the full PDF for all 30 answers with step-by-step solutions.

About This Worksheet

TopicPolynomials
BoardCBSE
Class10
Total Questions30 (10 Easy + 10 Medium + 10 Hard)
Answer KeyIncluded
PriceFree

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Frequently Asked Questions

Where can I download free polynomials sums for Class 10?+
You can download a free Polynomials PDF worksheet for Class 10 CBSE right here on SparkEd. The worksheet includes 30 practice questions (polynomials, degree, zeroes, factor theorem, remainder theorem, and factorisation of polynomials) at easy, medium, and hard levels with a complete answer key.
How many polynomials questions are in this Class 10 worksheet?+
This SparkEd worksheet for Polynomials Class 10 contains 30 questions — 10 easy, 10 medium, and 10 hard. The questions cover polynomials, degree, zeroes, factor theorem, remainder theorem, and factorisation of polynomials. A fresh set is generated daily so students never repeat the same sheet.
Does the Polynomials worksheet for Class 10 include answers?+
Yes! Every SparkEd worksheet comes with a complete answer key. Students can self-check their work after completing the sheet. The PDF is free to download and print.
Is this polynomials worksheet aligned to CBSE syllabus?+
Yes. This worksheet is specifically designed for Class 10 CBSE students and aligned to the 2025-26 CBSE syllabus. All questions follow the CBSE exam pattern and difficulty level.
Can I print this Polynomials worksheet?+
Absolutely! The worksheet downloads as an A4-size PDF that is ready to print. It includes the questions, space for working, and a separate answer key — perfect for classroom use or home practice.
How is this worksheet different from NCERT textbook exercises?+
SparkEd worksheets go beyond NCERT exercises by providing 30 questions at 3 progressive difficulty levels. Level 1 (Easy) builds confidence, Level 2 (Medium) tests application, and Level 3 (Hard) prepares for exams. Each worksheet includes word problems and conceptual questions, not just computation.

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SparkEd Maths provides free printable maths worksheets for Class 1-10 across CBSE, ICSE, IB, Olympiad, UP Board, Maharashtra SSC, and TN Board. Every worksheet includes an answer key and is aligned to the 2025-26 syllabus.