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Toggle## class 10 maths 2.1 solutions

# NCERT Solutions For Class 10 Maths Chapter 2 Polynomial Ex 2.1

Download the free NCERT Maths Chapter 2 Solutions for Class 10 here. Real Numbers in Maths Class 10 NCERT Solutions are a great resource for homework assistance. Ex 2.1 Maths Class 10 Chapter 2 Expert Bhautikstudy.com Teachers developed the NCERT Solutions. Complete solutions to all the problems in NCERT Textbook’s Chapter 2 Math Class 10 Real Numbers Exercise 2.1.

Class 10 Maths 2.1 Solutions Question 1.

**1. The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.**

## Maths in Class 10: Polynomial

### Introduction to Polynomials (In class 10 maths 2.1 solutions) :

In class 10 maths 2.1 solutions A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, but not division by a variable. It’s expressed in the form:

�(�)=����+��−1��−1+…+�1�+�0P(x)=anxn+an−1xn−1+…+a1x+a0

Where:

- ��,��−1,…,�1,�0an,an−1,…,a1,a0 are coefficients.
- �x is the variable.
- �n is a non-negative integer and is the degree of the polynomial.

### Types of Polynomials:

- Linear Polynomial: Degree 1. Example: 2�+32x+3.
- Quadratic Polynomial: Degree 2. Example: 3�2−5�+23x2−5x+2.
- Cubic Polynomial: Degree 3. Example: �3+2�2−�+5x3+2x2−x+5.
- Quartic Polynomial: Degree 4. Example: 4�4−3�2+2�−14x4−3x2+2x−1.
- Quintic Polynomial: Degree 5. Example: 5�5−�3+4�2−2�+75x5−x3+4x2−2x+7.
- Higher-Degree Polynomials: Degree more than 5.

### In class 10 maths 2.1 solutions Operations on Polynomials:

- Addition and Subtraction: Combine like terms.
- Multiplication: Distributive property.
- Division: Long division or synthetic division.

### Special Polynomials:

- Zero Polynomial: �(�)=0P(x)=0.
- Constant Polynomial: Degree 0, �(�)=�P(x)=a.
- Monomial: A polynomial with only one term.
- Binomial: A polynomial with two terms.
- Trinomial: A polynomial with three terms.

### Factoring Polynomials:

- Common Factor: Factor out the greatest common factor.
- Difference of Squares: �2−�2=(�+�)(�−�)a2−b2=(a+b)(a−b).
- Perfect Square Trinomial: �2+2��+�2=(�+�)2a2+2ab+b2=(a+b)2.
- Sum or Difference of Cubes: �3±�3=(�±�)(�2∓��+�2)a3±b3=(a±b)(a2∓ab+b2).
- Factoring by Grouping: Group terms and look for common factors.

### In class 10 maths 2.1 solutions Polynomial Equations:

Solving polynomial equations involves finding the values of the variable that make the polynomial expression equal to zero.

### Remainder Theorem and Factor Theorem:

- Remainder Theorem: If a polynomial �(�)P(x) is divided by �−�x−a, the remainder is �(�)P(a).
- Factor Theorem: If �(�)=0P(a)=0, then �−�x−a is a factor of �(�)P(x).

### Roots and Zeros:

- Roots: Values of �x that make �(�)=0P(x)=0.
- Zeros: Same as roots.

### Synthetic Division:

A method to divide polynomials by binomials of the form �−�x−a.

### Graphs of Polynomials:

- Degree and Behavior: The degree determines the behavior of the polynomial at its ends.
- Turning Points: Locations where the graph changes direction.
- End Behavior: Determined by the leading term.

### Application:

- In class 10 maths 2.1 solutions Polynomials are extensively used in various fields including physics, engineering, economics, and computer graphics.

These are fundamental notes on polynomials suitable for a class 10 level. They cover basic concepts, operations, factorization, equations, and application areas, Here class 10 maths 2.1 solutions play an important role.

In class 10 maths 2.1 solutions In several disciplines, including physics, engineering, economics, and computer graphics, polynomials are widely employed.

These are basic polynomial notes appropriate for a class 10 setting. They address fundamental ideas, procedures, factorization, equations, and application domains. class 10 maths 2.1 solutions are crucial in this context.

In Class 9, polynomials are introduced. In the last session, we covered polynomials in one variable and their degrees. Class 10 goes into additional information on this. This chapter’s NCERT Solutions for Class 10 Maths cover the solutions to a variety of polynomial-related problems and their uses. We examine the division procedure for polynomials of integers and investigate the relationship between the zeroes and coefficients of quadratic polynomials.

Important Elements of the NCERT Solutions for Math Class 10 Chapter 2: Polynomials

It covers the Maths Class 10 CBSE syllabus for 2024–2025.

You will feel sure about doing well on the tests after going over these NCERT Solutions, which have been produced by our subject matter specialists.

It adheres to NCERT criteria, which aid in appropriately preparing the pupils.

It includes every significant query from the perspective of the examination.