Class 10 Mathematics Chapter 9 Exercise 9.1 Solutions – Step-by-Step Guide

In this section, you will find detailed solutions to all questions in Exercise 9.1 of Class 10 Mathematics, Chapter 9. These questions will help you understand key concepts and prepare for exams effectively. Whether you're looking for quick answers or in-depth explanations, this guide provides a comprehensive understanding.

Sample Questions and Answers for Class 10 Maths Ch 9 Ex 9.1 Solution

Question 1:
If a polynomial has a degree of 3, what is the highest power of the variable in this polynomial?

Answer:
The highest power of the variable in a degree 3 polynomial is 3. This means the polynomial will include terms such as x³, x², x, and a constant.

Question 2:
Find the value of the polynomial 2x³ + 3x² - x + 4 when x = 1.

Answer:
Substituting x = 1 into the polynomial, we get:
2(1)³ + 3(1)² - 1 + 4 = 2 + 3 - 1 + 4 = 8.
Thus, the value is 8.

Question 3:
What is the sum of the polynomials (3x² + 2x - 4) and (5x² - x + 7)?

Answer:
Add the corresponding terms:
(3x² + 5x²) + (2x - x) + (-4 + 7) = 8x² + x + 3.
So, the sum is 8x² + x + 3.

Question 4:
Subtract the polynomial (4x³ - 3x² + 2x - 5) from (7x³ + 2x² - x + 3).

Answer:
Subtracting the polynomials:
(7x³ - 4x³) + (2x² + 3x²) + (-x - 2x) + (3 + 5) = 3x³ + 5x² - 3x + 8.
So, the result is 3x³ + 5x² - 3x + 8.

Question 5:
Find the value of the polynomial 4x² - 3x + 5 when x = -2.

Answer:
Substitute x = -2 into the polynomial:
4(-2)² - 3(-2) + 5 = 4(4) + 6 + 5 = 16 + 6 + 5 = 27.
Thus, the value is 27.

Question 6:
What do you get when you multiply the polynomials (x + 3) and (x - 2)?

Answer:
Using distributive property:
x(x - 2) + 3(x - 2) = x² - 2x + 3x - 6 = x² + x - 6.
So, the product is x² + x - 6.

Question 7:
If a polynomial has no x² term and the constant term is 5, what might the polynomial look like?

Answer:
The polynomial might look like x³ + 2x + 5, where the x² term is absent, and the constant is 5.

Question 8:
Simplify the expression: (3x + 5) + (4x - 7).

Answer:
Add the like terms:
(3x + 4x) + (5 - 7) = 7x - 2.
So, the simplified expression is 7x - 2.

Question 9:
Multiply the binomials (x + 4) and (x - 1).

Answer:
Using distributive property:
x(x - 1) + 4(x - 1) = x² - x + 4x - 4 = x² + 3x - 4.
So, the product is x² + 3x - 4.

Question 10:
Find the difference between the polynomials (2x² + 5x - 6) and (x² - 3x + 4).

Answer:
Subtract the polynomials:
(2x² - x²) + (5x + 3x) + (-6 - 4) = x² + 8x - 10.
So, the difference is x² + 8x - 10.

Question 11:
Evaluate the polynomial x² - 4x + 3 when x = 3.

Answer:
Substitute x = 3 into the polynomial:
(3)² - 4(3) + 3 = 9 - 12 + 3 = 0.
Thus, the value is 0.

Question 12:
What is the product of the polynomials (x + 2) and (x + 5)?

Answer:
Using distributive property:
x(x + 5) + 2(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.
So, the product is x² + 7x + 10.

Question 13:
What is the quotient when the polynomial 4x² - 2x + 6 is divided by 2x?

Answer:
Divide each term by 2x:
(4x² ÷ 2x) - (2x ÷ 2x) + (6 ÷ 2x) = 2x - 1 + 3/x.
So, the quotient is 2x - 1 + 3/x.

Question 14:
Add the polynomials (2x - 4) and (3x + 5).

Answer:
Add the like terms:
(2x + 3x) + (-4 + 5) = 5x + 1.
So, the sum is 5x + 1.

Question 15:
Multiply the binomials (2x + 3) and (x - 4).

Answer:
Using distributive property:
2x(x - 4) + 3(x - 4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.
So, the product is 2x² - 5x - 12.

Question 16:
Find the value of the polynomial 3x² + 2x - 7 when x = -1.

Answer:
Substitute x = -1 into the polynomial:
3(-1)² + 2(-1) - 7 = 3(1) - 2 - 7 = 3 - 2 - 7 = -6.
Thus, the value is -6.

Question 17:
What is the result when you subtract (3x² + x - 5) from (5x² - 2x + 4)?

Answer:
Subtract the polynomials:
(5x² - 3x²) + (-2x - x) + (4 + 5) = 2x² - 3x + 9.
So, the result is 2x² - 3x + 9.

Question 18:
Simplify the expression: 5x + 3x - 2x + 7.

Answer:
Combine the like terms:
5x + 3x - 2x = 6x, so the expression simplifies to 6x + 7.

Question 19:
Find the value of the polynomial x² + 2x - 1 when x = -3.

Answer:
Substitute x = -3 into the polynomial:
(-3)² + 2(-3) - 1 = 9 - 6 - 1 = 2.
Thus, the value is 2.

Question 20:
What is the sum of the polynomials (x² + 4x - 3) and (-x² + 2x + 5)?

Answer:
Add the corresponding terms:
(x² - x²) + (4x + 2x) + (-3 + 5) = 6x + 2.
So, the sum is 6x + 2.

Top Indian Books for Class 10 Maths Ch 9 Ex 9.1 Solution

"R.D. Sharma's Mathematics for Class 10"
Author: R.D. Sharma
Publication: Dhanpat Rai Publications
This book offers in-depth coverage of all topics for Class 10 Maths, with clear explanations and a variety of questions from basic to advanced levels. It provides solutions for Exercise 9.1 that are structured to build concepts step by step, ideal for self-practice.

"Mathematics for Class 10" by R.S. Aggarwal
Author: R.S. Aggarwal
Publication: S. Chand Publications
Known for its thorough approach, this book offers numerous questions based on various concepts and techniques. It covers the topics included in Exercise 9.1 and includes both solved examples and unsolved questions for better practice.

"Oswal Publishers Mathematics Class 10"
Author: Oswal Publishers
Publication: Oswal Publishers
This book features a variety of practice questions for all exercises, including Exercise 9.1. The clear and concise explanations and practice questions ensure a comprehensive understanding of the concepts.

"Exemplar Problems Class 10 Mathematics"
Author: NCERT
Publication: NCERT
This book offers an extensive set of problems that are meant to challenge students. The focus is on developing problem-solving skills and preparing students for competitive exams, with solutions related to Exercise 9.1.

"Mathematics Class 10" by Laxmi Publications
Author: Laxmi Publications
Publication: Laxmi Publications
This comprehensive guide provides clear solutions for all exercises. For Exercise 9.1, it includes step-by-step solutions for each problem, enhancing conceptual clarity and problem-solving skills.

"CBSE Chapterwise Solved Papers Class 10 Mathematics"
Author: Arihant Experts
Publication: Arihant Publications
The book is ideal for revision and practice. It contains previous years' solved question papers, which help students understand the pattern and type of questions, with specific exercises covering similar content to Exercise 9.1.

"M.L. Aggarwal’s Mathematics Class 10"
Author: M.L. Aggarwal
Publication: Vikas Publication House
This book provides a thorough understanding of algebra, geometry, and other topics, including those in Exercise 9.1. It is designed to help students develop a solid foundation and improve problem-solving skills.

"Target Mathematics Class 10" by J.S. Kaur
Author: J.S. Kaur
Publication: Target Publications
With detailed explanations of formulas and solutions for every exercise, this book is focused on making concepts easier for students to grasp. It includes several worked-out examples that help clarify Exercise 9.1.

"Comprehensive Mathematics for Class 10"
Author: Cengage Learning
Publication: Cengage Learning
This book offers a detailed explanation of all the topics in Class 10 Mathematics, including the chapters covered in Exercise 9.1. It is ideal for concept revision and practice of complex problems.

"Mathematics Class 10" by D.K. Agarwal
Author: D.K. Agarwal
Publication: New Age International Publishers
Known for its clear explanations and simple approach, this book provides solutions that enhance understanding. It includes a variety of problems that test a student's grasp of Exercise 9.1 and its application.

"Mathematics for Class 10 by R.D. Sharma"
Author: R.D. Sharma
Publication: Dhanpat Rai & Co.
This book focuses on different methods to solve problems and provides answers with clear steps. It covers everything from basic understanding to advanced application for exercises similar to Exercise 9.1.

"Mastering Mathematics for Class 10" by G.R. Kamat
Author: G.R. Kamat
Publication: G.R. Kamat Publications
The book is designed to ensure mastery of mathematical concepts. It includes detailed solutions to Exercise 9.1 and covers other mathematical techniques needed for comprehensive learning.

"Success Mathematics for Class 10"
Author: Success Publications
Publication: Success Publications
This guide offers an easy-to-understand approach to solving complex problems. It includes questions and solutions designed to prepare students for all kinds of mathematical challenges, including Exercise 9.1.

"S. Chand Mathematics Class 10"
Author: S. Chand Experts
Publication: S. Chand Publishing
This textbook provides a thorough breakdown of algebraic concepts and includes practice questions with solutions aligned with Exercise 9.1.

"I.M. Pandey Mathematics Class 10"
Author: I.M. Pandey
Publication: I.M. Pandey Publishers
This book is known for its well-structured content, presenting each topic with clear explanations and exercises similar to Exercise 9.1, offering plenty of practice for students.

"Mathematics Class 10" by P.K. Agarwal
Author: P.K. Agarwal
Publication: P.K. Agarwal Publications
With a focus on understanding rather than rote learning, this book provides practice problems, including those from Exercise 9.1, that aid in building a solid foundation in mathematics.

"S.Chand’s Practical Mathematics for Class 10"
Author: S.Chand Experts
Publication: S. Chand Publishing
A practical approach to learning mathematics, this book includes exercises from Exercise 9.1 and provides ample opportunities for students to practice problem-solving skills.

"NCERT Mathematics for Class 10"
Author: NCERT
Publication: NCERT
The NCERT books are widely used and provide an in-depth understanding of the subject. They cover all necessary exercises, including Exercise 9.1, and ensure strong conceptual knowledge for students.

"Mathematics Class 10" by Dinesh Publications
Author: Dinesh Publications
Publication: Dinesh Publications
This textbook includes detailed answers to all problems, with a particular focus on Exercises like 9.1. Its step-by-step approach helps students understand the process and solve complex problems.

"All in One Mathematics Class 10"
Author: Arihant Experts
Publication: Arihant Publications
Known for its practical approach, this book provides a series of important questions with detailed answers. It also includes answers for Exercise 9.1, aiding students with their learning process.

Class 10 Maths Ch 9 Ex 9.1 Solution: An Engaging Guide for Students

Class 10 Mathematics Chapter 9, Exercise 9.1, covers some essential algebraic concepts that form the foundation of higher mathematical studies. Exercise 9.1 is centered around polynomials, a crucial topic that frequently appears in exams, requiring students to understand the operations of addition, subtraction, and multiplication of polynomials.

This exercise helps students solidify their understanding of how to add, subtract, and multiply polynomials, along with evaluating them for given values of variables. For a strong grasp, it’s essential that students comprehend the methods of solving polynomial expressions, as these problems require logical thinking and step-by-step application of rules.

A key component of solving problems in Exercise 9.1 involves recognizing terms in a polynomial and performing operations on them systematically. The most common types of questions include the addition of polynomials, subtraction, and solving for specific values of variables. For instance, you might be asked to simplify expressions, evaluate them at given points, or even identify the degree of a polynomial.

To excel in Exercise 9.1, students should focus on understanding how to manipulate terms by grouping like terms and applying the distributive property when multiplying polynomials. The questions within this exercise are often structured to improve a student's problem-solving abilities, preparing them for more complex topics in algebra and even calculus in the future.

Books like those by R.D. Sharma, R.S. Aggarwal, and NCERT provide comprehensive explanations and a wide array of practice questions. These books ensure that students have enough material to practice and perfect their understanding of polynomials. With solutions to each problem, these texts guide learners step by step, offering detailed explanations for each solution.

Teachers often emphasize the importance of regular practice with such exercises. Students should practice each type of problem multiple times, as repetition is key to mastering polynomial operations.