by Tiwari Academy
Class 9 Maths Chapter 2 Solution for CBSE Board
Class 9 Maths Exercise 2.1 in English
Class 9 Maths Exercise 2.2 in English
Class 9 Maths Exercise 2.3 in English
Class 9 Maths Exercise 2.4 in English
Class 9 Maths Chapter 2 Solution for State Boards
Class 9 Maths Chapter 2 Exercise 2.1
Class 9 Maths Chapter 2 Exercise 2.2
Class 9 Maths Chapter 2 Exercise 2.3
Class 9 Maths Chapter 2 Exercise 2.4
Class 9 Maths Chapter 2 Exercise 2.5
In addition to solutions, Tiwari Academy may also provide practice questions and additional exercises related to each topic. This extra practice can be valuable for reinforcing learning and improving problem-solving skills.
Class 9 Maths Chapter 2 Solution in Hindi
Class 9 Maths Exercise 2.1 in Hindi
Class 9 Maths Exercise 2.2 in Hindi
Class 9 Maths Exercise 2.3 in Hindi
Class 9 Maths Exercise 2.4 in Hindi
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials in Hindi and English Medium revised and modified for academic year 2024-25. The solutions offered by Tiwari Academy often aim to simplify complex mathematical concepts, making it easier for students to understand and grasp the subject matter. Questions are based on latest NCERT books following new syllabus for 2024-25 exams.
NCERT Solutions for Class 9 Maths Chapter 2
| Class: 9 | Mathematics |
| Chapter 2: | Polynomials |
| Number of Exercises: | 4 (Four) |
| Content: | Chapter Exercises Solution |
| Mode: | Online Text and Videos |
| Academic Session: | 2024-25 |
| Medium: | English and Hindi Medium |
As per the Uttar Pradesh Board, Prayagraj – the NCERT Books are now implemented for class 9 Maths for 2024-25. So, the students of class 9 (High School) can download UP Board Solutions for Class 9 Maths Chapter 2 from the links given below. 9th Maths Chapter 2 Solutions are available in Hindi and English Medium.
Videos related to each exercise are also given below, which help the students to know the steps of solutions. Download NCERT (https://ncert.nic.in/) Solutions Apps and UP Board Solutions app 2024-25 and Offline Solutions based on latest Curriculum for 2024-25.
Study Materials on 9th Maths Chapter 2
Important Terms on 9th Maths Chapter 2
Important Questions on 9th Maths Chapter 2
Determine whether polynomials x³ + x² + x + 1 has x + 1 a factor?
Let p(x) = x³ + x² + x + 1 Putting x + 1 = 0, we get, x = – 1 Using remainder theorem, when p(x)= x³ + x² + x + 1 is divided by x + 1, remainder is given by p(-1) = (-1)³ + (-1)² + (-1) + 1 = – 1 + 1 – 1 + 1 = 0 Since, remainder p(-1) = 0, Hence x + 1 is a factor of x³ + x² + x + 1.
Use the Factor Theorem to determine whether g(x) is a factor of p(x): p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1.
p(x) = 2x³ + x² – 2x – 1 and g(x) = x + 1 Putting x + 1 = 0, we get, x = -1 Using remainder theorem, when p(x) = 2x³ + x² – 2x – 1 is divided by g(x) = x + 1, remainder is given by p(-1) = (-1)³ + (-1)² + (-1) + 1 = – 1 + 1 – 1 + 1 = 0 Since, remainder p(-1) = 0, hence g(x) is a factor of p(x).
Find the value of k, if x – 1 is a factor of p(x) = x² + x + k.
p(x) = x² + x + k Putting x – 1 = 0, we get, x = 1 Using remainder theorem, When p(x) = x² + x + k is divided by x – 1, remainder is given by p(1) = (1)² + (1) + k = 2 + k Since x – 1 is a factor of p(x), hence remainder p(1) = 0 ⇒ 2 + k = 0 ⇒ k = -2
Find the zero of the polynomial p(x) = x + 5.
p(x) = x + 5 Putting p(x) = 0, we get x + 5 = 0 ⇒ x = – 5 Hence, x = – 5 is a zero of the polynomial p(x).
1. A combination of constants and variables, connected by four fundamental arithmetical operations +, -, x and / is called an algebraic expression. e.g. 6x² – 5y² + 2xy
2. An algebraic expression which have only whole numbers as the exponent of one variable, is called polynomial in one variable. e.g. 3x³ + 2x² – 7x + 5 etc.
3. The part of a polynomial separated from each other by + or – sign is called a term and each term of a polynomial has a coefficient.
4. Highest power of the variable in a polynomial, is known as degree of that polynomial.
5. The value obtained on putting a particular value of the variable in polynomial is called value of the polynomial at the value of variable.
6. Zero of a polynomial p(x) is a number alpha, such that p(alpha) = 0. It is also called root pf polynomial equation p(x) = 0.
7. Let f(x) be any polynomial of degree n,(n ≥ 1) and a be any real number. If f(x) is divided by the linear polynomial (x-a), then the remainder is f(a).
8. Let f(x) be a polynomial of degree n,(n ≥ 1) and a be any real number. Then,
i). If f(a) = 0, then (x – a) is a factor of f(x).
ii). If (x – a) is a factor of f(x), then f(a) = 0.
Polynomial on the Basis of Number of Terms
Polynomial on the Basis of Number of Terms
A polynomial containing one non-zero term, is called a monomial.
A polynomial containing two non-zero terms, is called a binomial.
A polynomial containing three non-zero terms, is called a trinomial.
Polynomial on the Basis of Degree of Variables
A polynomial of degree 0, is called a constant polynomial.
A polynomial of degree 1, is called a linear polynomial.
A polynomial of degree 2, is called a quadratic polynomial.
A polynomial of degree 3, is called a cubic polynomial.
A polynomial of degree 4, is called a biquadratic polynomial.
What is the core motive of the chapter 2 Polynomials of class 9 Maths?
The core motive of chapter 2 Polynomials of class 9 Maths is to make the meaning of the following things clear to students.
- 1. Meaning of polynomials in one variable.
- 2. Terms of the polynomials.
- 3. Meaning of coefficients.
- 4. Meaning of zero polynomial.
- 5. Degree of the polynomial.
- 6. Types of the polynomial (Linear, Quadratic, Cubic).
- 7. Zeroes of a polynomial.
- 8. Factorization of polynomial, Factor theorem.
- 9. Algebraic identities.
Is the chapter 2 Polynomials of class 9th Maths complicated?
No, chapter 2 Polynomials of class 9th Maths is not that complicated. Basically, in exercises 2.3 and 2.4, most of the students face a little problem. Exercises 2.1, and 2.2 are quite easy compared to exercise 2.3 and 2.4.
How many exercises are there in 9th Maths Chapter 2 with least number of difficult questions?
In chapter 2 of class 9th Maths, there are four exercises. The first exercise (Ex 2.1) contains five questions, the second exercise (Ex 2.2) contains four questions, the third exercise contains five questions, and the fourth exercise (Ex 2.4) contains sixteen questions. So the second exercise (Ex 2.2) has the least number of questions.
How many theorems are there in the chapter 2 Polynomials of class 9 Maths?
There are two theorems (Remainder theorem and Factor theorem) in chapter 2 Polynomials of class 9 Maths. Both the theorems are important for the exams. The remainder theorem is used in exercise 2.3, and the Factor theorem is used in exercise 2.4.
