CBSE Class 10 Mathematics Polynomials Worksheet Set D

Read and download the CBSE Class 10 Mathematics Polynomials Worksheet Set D in PDF format. We have provided exhaustive and printable Class 10 Mathematics worksheets for Chapter 2 Polynomials, designed by expert teachers. These resources align with the 2025-26 syllabus and examination patterns issued by NCERT, CBSE, and KVS, helping students master all important chapter topics.

Chapter-wise Worksheet for Class 10 Mathematics Chapter 2 Polynomials

Students of Class 10 should use this Mathematics practice paper to check their understanding of Chapter 2 Polynomials as it includes essential problems and detailed solutions. Regular self-testing with these will help you achieve higher marks in your school tests and final examinations.

Class 10 Mathematics Chapter 2 Polynomials Worksheet with Answers

 

POLYNOMIALS

Q.- Give examples of polynomials p(x), q(x) and r(x), which satisfy the division algorithm and 
(i) deg p(x) = deg q(x) 
(ii) deg q(x) = deg r(x) 
(iii) deg q(x) = 0 
 
Sol. (i) Let q(x) = 3x2 + 2x + 6, degree of q(x) = 2 
p(x) = 12x2 + 8x + 24, degree of p(x) = 2 
Here, deg p(x) = deg q(x) 
 
(ii) p(x) = x5 + 2x4 + 3x3 + 5x2 + 2 
q(x) = x2 + x + 1, degree of q(x) = 2 
g(x) = x3 + x2 + x + 1 
r(x) = 2x2 – 2x + 1, degree of r(x) = 2 
Here, deg q(x) = deg r(x) 
 
(iii) Let p(x) = 2x4 + 8x3 + 6x2 + 4x + 12 
q(x) = 2, degree of q(x) = 0 
g(x) = x4 + 4x3 + 3x2 + 2x + 6 
r(x) = 0 
Here, deg q(x) = 0 
 
Q.- If the zeroes of polynomial x3 – 3x2 + x + 1  are a – b, a , a + b. Find a and b. 
 
Sol.  a – b, a, a + b are zeros 
∴ product (a – b) a(a + b) = –1 
=> (a2 – b2) a = –1                 …(1) 
and sum of zeroes is (a – b) + a + (a + b) = 3 
=> 3a = 3 => a = 1                …(2)
by (1) and (2)
(1 – b2)1 = –1
=> 2 = b2=> b = ± 2
∴ a = –1 & b = ± 2 Ans.
 
Q.-  If two zeroes of the polynomial x4 – 6x3 –26x2 + 138x – 35 are 2 ± √3 , find other zeroes.
 
Sol.  2 ± √3 are zeroes.
=> x = 2 ± √3
=> x – 2 = ± √3 (squaring both sides)
=> (x – 2)2 = 3
=> x2 + 4 – 4x – 3 = 0
=> x2 – 4x + 1 = 0 , is a factor of given polynomial
∴ other factors
polynomials notes 1
∴ other factors = x2 – 2x – 35
= x2 – 7x + 5x – 35 = x(x – 7) + 5(x – 7)
= (x – 7) (x + 5)
∴ other zeroes are (x – 7) = 0
=> x = 7
x + 5 = 0
=> x = – 5 Ans.
 
Q.- If the polynomial x4 – 6x3 + 16x2 –25x + 10 is divided by another polynomial x2 –2x + k, the remainder comes out to be x + a, find k & a.
 
Sol. 
polynomials notes 2
 
Q.-  Apply the division algorithm to find the quotient and remainder on dividing p(x) by g(x) as given below
p(x) = x4 – 3x2 + 4x + 5, g (x) = x2 + 1 – x
 
Sol. We have,
p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x
polynomials notes 3
We stop here since
degree of (8) < degree of (x2 – x + 1).
So, quotient = x2 + x – 3, remainder = 8
Therefore,
Quotient × Divisor + Remainder
= (x2 + x – 3) (x2 – x + 1) + 8
= x4 – x3 + x2 + x3 – x2 + x – 3x2 + 3x – 3 + 8
= x4 – 3x2 + 4x + 5 = Dividend
Therefore the Division Algorithm is verified.
 
Q.- Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm.t2 – 3; 2t4 + 3t3 – 2t2 – 9t – 12.
 
Sol. We divide 2t4 + 3t3 – 2t2 – 9t – 12 by t2 – 3
polynomials notes 4
Here, remainder is 0, so t2 – 3 is a factor of
2t4 + 3t3 – 2t2 – 9t – 12.
2t4 + 3t3 – 2t2 – 9t – 12 = (2t2 + 3t + 4) (t2 – 3)
 
Q.- Apply the division algorithm to find the quotient and remainder on dividing p(x) by g(x) as given below :
p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2
 
Sol. We have,
p(x) = x3 – 3x2 + 5x – 3 and g(x) = x2 – 2
 polynomials notes 5
We stop here since
degree of (7x – 9) < degree of (x2 – 2)
So, quotient = x – 3, remainder = 7x – 9
Therefore,
Quotient × Divisor + Remainder
= (x – 3) (x2 – 2) + 7x – 9
= x3 – 2x – 3x2 + 6 + 7x – 9
= x3 – 3x2 + 5x – 3 = Dividend
Therefore, the division algorithm is verified.
 

 

Please click the below link to access CBSE Class 10 Mathematics Polynomials Worksheet Set D

Chapter 01 Real Numbers
CBSE Class 10 Mathematics Real Numbers Worksheet Set A
CBSE Class 10 Mathematics Real Numbers Worksheet Set B
CBSE Class 10 Mathematics Real Numbers Worksheet Set C
CBSE Class 10 Mathematics Real Numbers Worksheet Set D
CBSE Class 10 Mathematics Real Numbers Worksheet Set E
CBSE Class 10 Mathematics Real Numbers Worksheet Set F
CBSE Class 10 Mathematics Real Numbers Worksheet Set G
Chapter 02 Polynomials
CBSE Class 10 Mathematics Polynomials Worksheet Set A
CBSE Class 10 Mathematics Polynomials Worksheet Set B
CBSE Class 10 Mathematics Polynomials Worksheet Set C
CBSE Class 10 Mathematics Polynomials Worksheet Set D
CBSE Class 10 Mathematics Polynomials Worksheet Set E
CBSE Class 10 Mathematics Polynomials Worksheet Set F
CBSE Class 10 Mathematics Polynomials Worksheet Set G
CBSE Class 10 Mathematics Polynomials Worksheet Set H
CBSE Class 10 Mathematics Polynomials Worksheet Set I
CBSE Class 10 Mathematics Polynomials Worksheet Set J
CBSE Class 10 Mathematics Polynomials Worksheet Set K
Chapter 03 Pair of Linear Equations in Two Variables
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set A
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set B
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set C
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set D
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set E
CBSE Class 10 Mathematics Pair Of Linear Equations In 2 Variables Worksheet Set F
Chapter 04 Quadratic Equation
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set A
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set C
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set D
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set E
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set F
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set I
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set J
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set K
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set L
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set M
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set N
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set O
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set P
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set Q
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set R
CBSE Class 10 Mathematics Quadratic Equation Worksheet Set S
Chapter 05 Arithmetic Progression
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set A
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set B
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set C
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set D
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set E
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set F
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set G
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set H
CBSE Class 10 Mathematics Arithmetic Progression Worksheet Set I
Chapter 06 Triangles
CBSE Class 10 Mathematics Triangles Worksheet Set A
CBSE Class 10 Mathematics Triangles Worksheet Set B
CBSE Class 10 Mathematics Triangles Worksheet Set C
CBSE Class 10 Mathematics Triangles Worksheet Set D
CBSE Class 10 Mathematics Triangles Worksheet Set E
CBSE Class 10 Mathematics Triangles Worksheet Set F
CBSE Class 10 Mathematics Triangles Worksheet Set G
CBSE Class 10 Mathematics Triangles Worksheet Set H
Chapter 07 Coordinate Geometry
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set A
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set B
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set C
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set D
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set E
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set F
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set G
CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set H
Chapter 08 Introduction to Trigonometry
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set A
CBSE Class 10 Mathematics Introduction to Trigonometry Worksheet Set B
Chapter 09 Some Applications of Trigonometry
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set A
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set B
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set C
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set D
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set E
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set F
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set G
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set H
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set I
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set J
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set K
CBSE Class 10 Mathematics Some Applications of Trigonometry Worksheet Set L
Chapter 10 Circles
CBSE Class 10 Mathematics Circles Worksheet Set A
CBSE Class 10 Mathematics Circles Worksheet Set B
CBSE Class 10 Mathematics Circles Worksheet Set C
CBSE Class 10 Mathematics Circles Worksheet Set D
CBSE Class 10 Mathematics Circles Worksheet Set E
CBSE Class 10 Mathematics Circles Worksheet Set F
CBSE Class 10 Mathematics Circles Worksheet Set G
CBSE Class 10 Mathematics Circles Worksheet Set H
Chapter 11 Areas related to Circles
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set A
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set B
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set C
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set D
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set E
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set F
CBSE Class 10 Mathematics Areas Related To Circles Worksheet Set G
Chapter 12 Surface Areas and Volumes
CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set A
CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set B
CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set C
Chapter 13 Statistics
CBSE Class 10 Mathematics Statistics Worksheet Set A
CBSE Class 10 Mathematics Statistics Worksheet Set B
CBSE Class 10 Mathematics Statistics Worksheet Set C
CBSE Class 10 Mathematics Statistics Worksheet Set D
CBSE Class 10 Mathematics Statistics Worksheet Set E
CBSE Class 10 Mathematics Statistics Worksheet Set F
CBSE Class 10 Mathematics Statistics Worksheet Set G
CBSE Class 10 Mathematics Statistics Worksheet Set H
CBSE Class 10 Mathematics Statistics Worksheet Set I
CBSE Class 10 Mathematics Statistics Worksheet Set J
Chapter 14 Probability
CBSE Class 10 Mathematics Probability Worksheet Set A
CBSE Class 10 Mathematics Probability Worksheet Set B
CBSE Class 10 Mathematics Probability Worksheet Set C
Other Topics
Case Study Chapter 1 Real Numbers Mathematics
Case Study Chapter 2 Polynomials Mathematics
Case Study Chapter 3 Linear Equations Mathematics
Case Study Chapter 6 Triangles Mathematics
Case Study Chapter 7 Coordinate Geometry Mathematics
Case Study Chapter 8 Trigonometry Mathematics
Case Study Chapter 11 Areas related to Circles Mathematics
Case Study Chapter 14 Probability Mathematics
CBSE Class 10 Mathematics Number Systems Worksheet

Important Practice Resources for Class 10 Mathematics

CBSE Mathematics Class 10 Chapter 2 Polynomials Worksheet

Students can use the practice questions and answers provided above for Chapter 2 Polynomials to prepare for their upcoming school tests. This resource is designed by expert teachers as per the latest 2026 syllabus released by CBSE for Class 10. We suggest that Class 10 students solve these questions daily for a strong foundation in Mathematics.

Chapter 2 Polynomials Solutions & NCERT Alignment

Our expert teachers have referred to the latest NCERT book for Class 10 Mathematics to create these exercises. After solving the questions you should compare your answers with our detailed solutions as they have been designed by expert teachers. You will understand the correct way to write answers for the CBSE exams. You can also see above MCQ questions for Mathematics to cover every important topic in the chapter.

Class 10 Exam Preparation Strategy

Regular practice of this Class 10 Mathematics study material helps you to be familiar with the most regularly asked exam topics. If you find any topic in Chapter 2 Polynomials difficult then you can refer to our NCERT solutions for Class 10 Mathematics. All revision sheets and printable assignments on studiestoday.com are free and updated to help students get better scores in their school examinations.

Where can I download the 2025-26 CBSE printable worksheets for Class 10 Mathematics Chapter Chapter 2 Polynomials?

You can download the latest chapter-wise printable worksheets for Class 10 Mathematics Chapter Chapter 2 Polynomials for free from StudiesToday.com. These have been made as per the latest CBSE curriculum for this academic year.

Are these Chapter Chapter 2 Polynomials Mathematics worksheets based on the new competency-based education (CBE) model?

Yes, Class 10 Mathematics worksheets for Chapter Chapter 2 Polynomials focus on activity-based learning and also competency-style questions. This helps students to apply theoretical knowledge to practical scenarios.

Do the Class 10 Mathematics Chapter Chapter 2 Polynomials worksheets have answers?

Yes, we have provided solved worksheets for Class 10 Mathematics Chapter Chapter 2 Polynomials to help students verify their answers instantly.

Can I print these Chapter Chapter 2 Polynomials Mathematics test sheets?

Yes, our Class 10 Mathematics test sheets are mobile-friendly PDFs and can be printed by teachers for classroom.

What is the benefit of solving chapter-wise worksheets for Mathematics Class 10 Chapter Chapter 2 Polynomials?

For Chapter Chapter 2 Polynomials, regular practice with our worksheets will improve question-handling speed and help students understand all technical terms and diagrams.