#### Chapters

▶ Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equations in two Variables

Chapter 5: Introduction to Euclid's Geometry

Chapter 6: Lines and Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Areas of Parallelograms and Triangles

Chapter 10: Circles

Chapter 11: Constructions

Chapter 12: Heron's Formula

Chapter 13: Surface Area and Volumes

Chapter 14: Statistics

Chapter 15: Probability

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## Solutions for Chapter 2: Polynomials

Below listed, you can find solutions for Chapter 2 of CBSE NCERT for Mathematics Class 9.

### NCERT solutions for Mathematics Class 9 Chapter 2 Polynomials Exercise 2.1 [Page 32]

**Which of the following expression is polynomial in one variable and which is not? State the reason for your answer.**

4x^{2} - 3x + 7

**Which of the following expression is polynomial in one variable and which is not? State the reason for your answer.**

`y^2+sqrt2`

**Which of the following expression is polynomial in one variable and which is not? State the reason for your answer.**

`3sqrtt+tsqrt2`

`y+2/y`

`x^10+y^3+t^50`

Write the coefficient of x^{2} in the following:-

`2+x^2+x`

Write the coefficient of x^{2} in the following:-

`2-x^2+x^3`

Write the coefficient of x^{2} in the following:-

`pi/2x^2+x`

Write the coefficient of x^{2} in the following:-

`sqrt2x-1`

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

Write the degree of the following polynomial:-

5x^{3} + 4x^{2} +7x

Write the degree of the following polynomial:-

4 - y^{2}

Write the degree of the following polynomials:-

`5t - sqrt7`

Write the degree of each of the following polynomials:-

3

**Classify the following as linear, quadratic, and cubic polynomials:**

x^{2} + x

**Classify the following as linear, quadratic, and cubic polynomials:**

x - x^{3}

**Classify the following as linear, quadratic, and cubic polynomials:**

y + y^{2} + 4

**Classify the following as linear, quadratic, and cubic polynomials:**

1 + x

**Classify the following as linear, quadratic, and cubic polynomials:**

3t

**Classify the following as linear, quadratic, and cubic polynomials:**

r^{2}

**Classify the following as linear, quadratic, and cubic polynomials:**

7x^{3}

### NCERT solutions for Mathematics Class 9 Chapter 2 Polynomials Exercise 2.2 [Pages 34 - 35]

Find the value of the polynomial 5x – 4x^{2} + 3 at

x = 0

Find the value of the polynomial 5x – 4x^{2} + 3 at

x = –1

Find the value of the polynomial 5x – 4x^{2} + 3 at

x = 2

Find p(0), p(1) and p(2) for the following polynomials:-

p(y) = y^{2} – y + 1

Find p(0), p(1) and p(2) for the following polynomials:-

p(t) = 2 + t + 2t^{2} – t^{3}

Find p(0), p(1) and p(2) for the following polynomials:-

p(x) = x^{3}

Find p(0), p(1) and p(2) for the following polynomials:-

p(x) = (x – 1) (x + 1)

Verify whether the following zeroes of the polynomial, indicated against them.

`p(x) = 3x + 1; x = -1/3`

Verify whether the following zeroes of the polynomial are indicated against them.

p(x) = 5x – π, `x = 4/5`

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = x^{2} – 1, x = 1, –1

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = (x + 1) (x – 2), x = – 1, 2

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = x^{2}, x = 0

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = lx + m, `x = – m/l`

Verify whether the following zeroes of the polynomial, indicated against them.

`p(x) = 3x^2 – 1, x = -1/sqrt3,2/sqrt3`

Verify whether the following zeroes of the polynomial, indicated against them.

p(x) = 2x + 1, `x = 1/2`

Find the zero of the polynomial in the following case:- p(x) = x + 5

Find the zero of the polynomial in the following case:- p(x) = x – 5

Find the zero of the polynomial in the following case:- p(x) = 2x + 5

Find the zero of the polynomial in the following case:- p(x) = 3x – 2

Find the zero of the polynomial in the following case:- p(x) = 3x

Find the zero of the polynomial in the following case:-

p(x) = ax, a ≠ 0

Find the zero of the polynomial in the following case:- p(x) = cx + d, c ≠ 0, c, d are real numbers.

### NCERT solutions for Mathematics Class 9 Chapter 2 Polynomials Exercise 2.3 [Page 40]

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by x+1.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by `x - 1/2`

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by x.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by x + π.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by 5 + 2x.

Find the remainder when x^{3} – ax^{2} + 6x – a is divided by x – a.

Check whether 7 + 3x is a factor of 3x^{3} + 7x.

### NCERT solutions for Mathematics Class 9 Chapter 2 Polynomials Exercise 2.4 [Pages 43 - 44]

Determine if the following polynomial has (x + 1) a factor :-

x^{3} + x^{2} + x + 1

Determine if the following polynomial has (x + 1) a factor :-

x^{4} + x^{3} + x^{2} + x + 1

Determine which of the following polynomials has (x + 1) a factor :-

x^{4} + 3x^{3} + 3x^{2} + x + 1

Determine which of the following polynomials has (x + 1) a factor :-

`x^3-x^2-(2+sqrt2)x+sqrt2`

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

p(x) = 2x^{3} + x^{2} – 2x – 1, g(x) = x + 1

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

*p*(*x*) = *x*^{3} + 3*x*^{2} + 3*x* + 1, *g*(*x*) = *x* + 2

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:-

*p*(*x*) = *x*^{3} − 4*x*^{2} + *x* + 6, *g*(*x*) = *x* − 3

Find the value of k, if x – 1 is a factor of p(x) in the following case:- p(x) = x^{2} + x + k

Find the value of k, if x – 1 is a factor of p(x) in the following case:-

`p(x) = 2x^2+kx+sqrt2`

Find the value of k, if x – 1 is a factor of p(x) in the following case:- `p(x) = kx^2 - sqrt2x +1`

Find the value of k, if x – 1 is a factor of p(x) in the following case:-

p(x) = kx^{2} – 3x + k

Factorise :- 12x^{2} – 7x + 1

Factorise :- 2x^{2} + 7x + 3

Factorise :- 6x^{2} + 5x – 6

Factorise :- 3x^{2} – x – 4

Factorise :- x^{3} – 2x^{2} – x + 2

Factorise :- x^{3} – 3x^{2} – 9x – 5

Factorise :- x^{3} + 13x^{2} + 32x + 20

Factorise :- 2y^{3} + y^{2} – 2y – 1

### NCERT solutions for Mathematics Class 9 Chapter 2 Polynomials Exercise 2.5 [Pages 48 - 50]

Use suitable identities to find the following products :- (x + 4) (x + 10)

Use suitable identities to find the following products :- (x + 8) (x – 10)

Use suitable identities to find the following products :- (3x + 4) (3x – 5)

Use suitable identities to find the following products :-

`(y^2+3/2)(y^2-3/2)`

Use suitable identities to find the following products :- (3 – 2x) (3 + 2x)

Evaluate the following product without multiplying directly:- 103 × 107

Evaluate the following product without multiplying directly:- 95 × 96

Evaluate the following product without multiplying directly:- 104 × 96

Factorise the following using appropriate identities:- 9x^{2} + 6xy + y^{2}

Factorise the following using appropriate identities:- 4y^{2} – 4y + 1

Factorise the following using appropriate identities:- `x^2 - y^2/100`

Expand following, using suitable identities :- (x + 2y + 4z)^{2 }

Expand following, using suitable identities :- (2x – y + z)^{2}

Expand following, using suitable identities :- (–2x + 3y + 2z)^{2}

Expand following, using suitable identities :- (3a – 7b – c)^{2}

Expand following, using suitable identities :- (–2x + 5y – 3z)^{2}

Expand following, using suitable identities :-`[1/4a-1/2b+1]^2`

Factorise:- 4x^{2} + 9y^{2} + 16z^{2} + 12xy – 24yz – 16xz

Factorise:- `2x^2+y^2+8z^2-2sqrt2xy+4sqrt2yz-8xz`

Write the following cube in expanded form:- (2x + 1)^{3}

Write the following cube in expanded form:- (2a – 3b)^{3}

Write the following cube in expanded form:- `[3/2x+1]^3`

Write the following cube in expanded form:- `[x-2/3y]^3`

Evaluate the following using suitable identities:-

(99)^{3}

Evaluate the following using suitable identities:- (102)^{3}

Evaluate the following using suitable identities:- (998)^{3}

Factorise :- 8a^{3} + b^{3} + 12a^{2}b + 6ab^{2}

Factorise :- 8a^{3} – b^{3} – 12a^{2}b + 6ab^{2}

Factorise :- 27 – 125a^{3} – 135a + 225a^{2}

Factorise :- 64a^{3} – 27b^{3} – 144a^{2}b + 108ab^{2}

Factorise :-

`27p^3-1/216-9/2p^2+1/4p`

Verify :- x^{3} + y^{3} = (x + y) (x^{2} – xy + y^{2})

Verify :- x^{3} – y^{3} = (x – y) (x^{2} + xy + y^{2})

Factorise :- 27y^{3} + 125z^{3}

Factorise :- 64m^{3} – 343n^{3}

Factorise :- 27x^{3} + y^{3} + z^{3} – 9xyz

Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`

If x + y + z = 0, show that x^{3} + y^{3} + z^{3} = 3xyz.

Without actually calculating the cubes, find the value of the following:- (–12)^{3} + (7)^{3} + (5)^{3}

Without actually calculating the cubes, find the value of the following:- (28)^{3} + (–15)^{3} + (–13)^{3}

Give possible expressions for the length and breadth of the following rectangle, in which their areas are given:-

Area : 25a^{2} – 35a + 12 |

Give possible expressions for the length and breadth of the following rectangle, in which their areas are given:-

Area : 35y^{2} + 13y –12 |

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

Volume : 3x^{2} – 12x |

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

Volume : 12ky^{2} + 8ky – 20k |

## Solutions for Chapter 2: Polynomials

## NCERT solutions for Mathematics Class 9 chapter 2 - Polynomials

Shaalaa.com has the CBSE Mathematics Mathematics Class 9 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Mathematics Class 9 CBSE 2 (Polynomials) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics Class 9 chapter 2 Polynomials are Algebraic Identities, Algebraic Identities, Polynomials, Polynomials in One Variable, Zeroes of a Polynomial, Remainder Theorem, Factorisation of Polynomials, Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0., Algebraic Identities, Polynomials, Polynomials in One Variable, Zeroes of a Polynomial, Remainder Theorem, Factorisation of Polynomials, Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0..

Using NCERT Mathematics Class 9 solutions Polynomials exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics Class 9 students prefer NCERT Textbook Solutions to score more in exams.

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