NCERT Solutions for Class 9 Maths Chapter 2: Polynomials

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The NCERT Solutions for Class 9 Maths Chapter 2 Polynomials are provided in this article. A polynomial is an expression composed of variables and coefficients that contain fundamental arithmetic operations such as addition, subtraction, and multiplication, as well as the exponential negative exponential of variables.

Chapter 2 Polynomials belongs to Unit 2 Algebra which has a weightage of 20 marks in the CBSE Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 2 cover the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 2 pdf

NCERT Solutions for Class 9 Maths Chapter 2

Class 9 Chapter 2 NCERT Solutions are given below:

Important Topics in Class 9 Maths Chapter 2 Polynomials

Important Topics in Class 9 Maths Chapter 2 Polynomials are elaborated below:

Remainder Theorem

Remainder Theorem is an Euclidean approach of division of polynomials. It says that if we divide a polynomial P(x) by a factor ( x – a); which is not necessarily an element of the polynomial; then we can find a smaller polynomial along with a remainder.

Example: Assume that f(a) = a³-12a²-42 is divided by (a-3). The quotient will be a²-9a-27 and the remainder is -123. Determine whether it satifies the Reaminder Theorem?

Solution: First let’s put a-3 = 0
Then, a = 3
Therefore, f(a) = f(3) = -123
Hence, it satisfies the remainder theorem.

Degree of Polynomial

Degree of a polynomial is known to be the greatest exponent of a variable in the polynomial.

Example: Determine the degree of polynomial: 3x⁸+ 4x³ + 9x + 1.

Solution: As pe the question, the degree of the polynomial, 3x⁸+ 4x³ + 9x + 1 is 8.

Algebraic Identities

Algebraic identities are equations that are valid for every value of variables in them. Algebraic identities are also widely used for the factorization of polynomials.

A few examples of Algebraic Identities:

(x + y)² = x² + 2xy + y²
(x – y)² = x² – 2xy + y²
x² – y² = (x + y) (x – y)
(x + a) (x + b) = x² + (a + b)x + ab.
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
(x + y)³ = x³ + y³ + 3xy(x + y)

Polynomials in One Variable

Polynomials in one variable are simply algebraic expressions. These can be found in axn, where n is a non-negative integer (i.e. positive or zero) and a is a real number, also known as the coefficient of the term.

Example:

P(x) = 4x – 3
G(y) = y⁴ – y²+ 2y + 9

Factorisation of Polynomials

Polynomials can also be represented as the product of its factors with a degree less than or equal to the original polynomial. In other words, the method of factoring is called factorization of polynomials.

Example: Factorise the Polynomial: x⁴ – 16.

Solution: Let’s consider the following
x⁴ – 16 = (x² + 4) (x² – 4)
Now, we can factorise (x²-4). Hence, the factorization will be,
x⁴ – 16 = (x² + 4) (x + 2) (x – 2)

NCERT Solutions for Class 9 Maths Chapter 2 Exercises:

The detailed solutions for all the NCERT Solutions for Real Numbers under different exercises are:

Read More:

Unit Related Topics
Polynomials in One Variable	Factorisation of Polynomials	Algebraic Identities
Remainder Theorem	Synthetic Division	Remainder

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Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
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CBSE X Related Questions

1.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.
View Solution
2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is
- $1$
- $-5$
- $25$
- $\sqrt{5}$
View Solution
3.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
View Solution
4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.
View Solution
5.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution
6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is
- $50^\circ$
- $60^\circ$
- $45^\circ$
- $30^\circ$
View Solution

View All

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NCERT Solutions for Class 9 Maths Chapter 2: Polynomials

NCERT Solutions for Class 9 Maths Chapter 2

Important Topics in Class 9 Maths Chapter 2 Polynomials

NCERT Solutions for Class 9 Maths Chapter 2 Exercises:

CBSE X Related Questions

1.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

Similar Mathematics Concepts

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NCERT Solutions for Class 9 Maths Chapter 2: Polynomials

NCERT Solutions for Class 9 Maths Chapter 2

Important Topics in Class 9 Maths Chapter 2 Polynomials

NCERT Solutions for Class 9 Maths Chapter 2 Exercises:

CBSE X Related Questions

1.In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

2.The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

4.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

6.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In the given figure, point D divides the side BC of $\Delta ABC$ in the ratio $1 : 2$. Find length AD.

2.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

3.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

4.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

5.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

6.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is