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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Math Study Guides
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.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

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2.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

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3.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

View Solution

4.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them
Monthly consumption
(in units)
Number of consumers
65 - 85
4
85 - 105
5
105 - 125
13
125 - 145
20
145 - 165
14
165 - 185
8
185 - 205
4

Monthly consumption (in units)	Number of consumers
65 - 85	4
85 - 105	5
105 - 125	13
125 - 145	20
145 - 165	14
165 - 185	8
185 - 205	4

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5.
Form the pair of linear equations for the following problems and find their solution by substitution method.
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km.
(v) A fraction becomes\(\frac{ 9}{11}\), if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes \(\frac{5}{6}\). Find the fraction.
(vi) Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?

View Solution

6.
Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

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You can also check

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.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

3.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

6.
Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

Similar Mathematics Concepts

Comments

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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. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

3. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

4. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare themMonthly consumption (in units) Number of consumers65 - 85 485 - 1055105 - 12513125 - 14520145 - 16514165 - 1858185 - 2054

6. Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

3.
A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

6.
Check whether \(6n\) can end with the digit \(0\) for any natural number \(n\).