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NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1 - Polynomials

NCERT Solutions for Class 9 Maths Chapter 2 Exercise 2.1 - Polynomials

Updated on May 02, 2025 04:13 PM IST

Polynomials exist as algebraic expressions which combine variables with constants using the addition and subtraction operations and multiplication and non-negative integer exponent operations. It educates us about how to identify polynomials and their degrees while differentiating between polynomial terms, together with their coefficients and classifications (monomial, binomial and trinomial).

This Story also Contains
  1. NCERT Solutions Class 9 Maths Chapter 2: Exercise 2.1
  2. Topics Covered in Chapter 2 Polynomials: Exercise 2.1
  3. NCERT Solutions of Class 9 Subject Wise
  4. NCERT Exemplar Solutions of Class 9 Subject Wise

Students can use the NCERT Solutions for Exercise 2.1 Class 9 Maths chapter 2 polynomials. The composition of the word "Polynomial" combines "Poly" for its multiple meanings with "nominal" as a term in this context to produce "many terms", as we learned in earlier sessions. The Exercise 2.1 Class 9 Maths chapter presents multiple problems at the start of the book. This section addresses the topic of polynomials through the NCERT Books.

NCERT Solutions Class 9 Maths Chapter 2: Exercise 2.1

Q1 (i) Is the following expression polynomial in one variable? State reasons for your answer. 4x23x+7

Answer:

Yes, given the polynomial 4x23x+7 has only one variable, which is x that is why it is a polynomial in one variable.

Q1 (ii) Is the following expression polynomial in one variable? State reasons for your answer. y2+2

Answer:

Yes, the given polynomial has only one variable, which is y, that is why it is a polynomial in one variable.

Q1 (iii) Is the following expression polynomial in one variable? State reasons for your answer. 3t+t2

Answer:

No, because we can observe that the exponent of variable t in the term 3t is 12, which is not a whole number.
Therefore, the expression given is not a polynomial.

Q1 (iv) Is the following expression polynomial in one variable? State reasons for your answer. y+2y

Answer:

No, because we can observe that the exponent of variable y in the term 2y is 1, which is not a whole number. Therefore, the given expression is not a polynomial.

Q1 (v) Is the following expression polynomial in one variable? State reasons for your answer. x10+y3+t50

Answer:

No, because in the given polynomial x10+y3+t50 there are 3 variables which are x, y, t. Therefore, the polynomial is not in one variable but in three variables.

Q2 (i) Write the coefficients of x2 in the following: 2+x2+x

Answer:

Coefficient of x2 in polynomial 2+x2+x is 1.

Q2 (ii) Write the coefficients of x2 in the following: 2x2+x3

Answer:

Coefficient of x2 in polynomial 2x2+x3 is -1.

Q2 (iii) Write the coefficients of x2 in the following: π2x2+x

Answer:

Coefficient of x2 in polynomial π2x2+x is π2.

Q2 (iv) Write the coefficients of x2 in the following: 2x1

Answer:

Coefficient of x2 in polynomial 2x1 is 0.

Q3 Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer:

The degree of a polynomial is the highest power of its variable.

In binomial, there are two terms: Therefore, a binomial of degree 35 is Eg: x35+1

In a monomial, there is only one term. Therefore, a monomial of degree 100 can be written as y100.

Q4 (i) Write the degree the following polynomial: 5x3+4x2+7x

Answer:

The degree of a polynomial is the highest power of its variable. Therefore, the degree of the polynomial 5x3+4x2+7x is 3.

Q4 (ii) Write the degree the following polynomial: 4y2

Answer:

The degree of a polynomial is the highest power of its variable. Therefore, the degree of the polynomial 4y2 is 2.

Q4 (iii) Write the degree the following polynomial: 5t7

Answer:

The degree of a polynomial is the highest power of its variable. Therefore, the degree of the polynomial 5t7 is 1.

Q4 (iv) Write the degree the following polynomial: 3

Answer:

The degree of a polynomial is the highest power of its variable. In this case, only a constant value 3 is there, and the degree of a constant polynomial is always 0.

Q5 (i) Classify the following as linear, quadratic and cubic polynomial: x2+x

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. The given polynomial is x2+x with degree 2. Therefore, it is a quadratic polynomial.

Q5 (ii) Classify the following as linear, quadratic and cubic polynomial: xx3

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. The given polynomial is xx3 with degree 3. Therefore, it is a cubic polynomial.

Q5 (iii) Classify the following as linear, quadratic and cubic polynomial: y+y2+4

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. The given polynomial is y+y2+4 with degree 2. Therefore, it is a quadratic polynomial.

Q5 (iv) Classify the following as linear, quadratic and cubic polynomial: 1+x

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. Given polynomial is 1+x with degree 1. Therefore, it is a linear polynomial.

Q5 (v) Classify the following as linear, quadratic and cubic polynomial: 3t

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. The given polynomial is 3t with degree 1. Therefore, it is a linear polynomial.

Q5 (vi) Classify the following as linear, quadratic and cubic polynomial: r2

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. The given polynomial is r2 with degree 2. Therefore, it is a quadratic polynomial.

Q5 (vii) Classify the following as linear, quadratic and cubic polynomial: 7x3

Answer:

Linear, quadratic, and cubic polynomials have degrees of 1, 2, and 3, respectively. The given polynomial is 7x3 with degree 3. Therefore, it is a cubic polynomial.


Also Read-

Topics Covered in Chapter 2 Polynomials: Exercise 2.1

  • Definition and recognition of polynomials: A polynomial is a mathematical expression made up of variables, constants, and exponents combined using addition, subtraction, or multiplication. It does not include division by a variable or negative exponents.
  • Variables, constants, coefficients, and terms: Variables are letters like x or y. Constants are fixed numbers. Coefficients are numbers multiplied by variables, like 4 in 4x. Terms are parts of a polynomial separated by plus or minus signs.
  • Types of polynomials (monomial, binomial, trinomial): Monomial has one term, Binomial has two terms and Trinomial has three terms
  • Degree of a polynomial: The degree is the highest power of the variable in a polynomial.
  • Identification of valid polynomials: A valid polynomial consists of an algebraic expression that contains variables, whole number exponents which are non-negative values. The valid polynomial does not contain square roots together with fractional variables and expressions with negative powers.
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NCERT Solutions of Class 9 Subject Wise

Students must check the NCERT solutions for class 9 of the Mathematics and Science Subjects.

NCERT Exemplar Solutions of Class 9 Subject Wise

Students must check the NCERT Exemplar solutions for class 9 of the Mathematics and Science Subjects.

Frequently Asked Questions (FAQs)

1. Can we say y + 3/y is a Polynomial?

No, we can't say the given term a Polynomial, because it does not follow the fundamental definition of Polynomial

2. Is Introductory exercise exercise 2.1 in chapter 2 important?

There are a total of 5 exercises in chapter 2 i.e. Ex 2.1, 2.2, 2.3, 2.4, 2.5, hence knowledge of preceding exercise make it more effective for students to understand more.

3. What are the attached topics related to chapter 2?

Well there are many more topics like a polynomial in one variable, remainder theorem, factorization, and algebraic identities 

4. Can you give an example of a monomial?

 Monomial is a type of polynomial that contains only one term example =  ax²

5. Can you give an example of binomial?

Binomial is a type of polynomial that contains only 2 terms example =  ax² + b  

6. What is the degree of polynomial x² +x?

The highest power of  x² +x is 2

Therefore degree = 2 hence it is a quadratic polynomial

7. What does polynomial with degree = 4 called?

A polynomial with degree  = 4 is called bi quadratic  polynomial, which is not in the course of chapter 2 Class 9

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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