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
Chapter 2: Polynomials
NCERT solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.1, Exercise 21.00 [Page 32]
Which of the following expression is polynomial in one variable and which is not? State the reason for your answer.
4x2 - 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`
Which of the following expression is polynomial in one variable and which is not? State the reason for your answer.
`y+2/y`
Which of the following expression is polynomial in one variable and which is not? State the reason for your answer.
`x^10+y^3+t^50`
Write the coefficient of x2 in the following:-
`2+x^2+x`
Write the coefficient of x2 in the following:-
`2-x^2+x^3`
Write the coefficient of x2 in the following:-
`pi/2x^2+x`
Write the coefficient of x2 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:-
5x3 + 4x2 +7x
Write the degree of the following polynomial:-
4 - y2
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:
x2 + x
Classify the following as linear, quadratic, and cubic polynomials:
x - x3
Classify the following as linear, quadratic, and cubic polynomials:
y + y2 + 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:
r2
Classify the following as linear, quadratic, and cubic polynomials:
7x3
NCERT solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.2 [Pages 34 - 35]
Find the value of the polynomial 5x – 4x2 + 3 at
x = 0
Find the value of the polynomial 5x – 4x2 + 3 at
x = –1
Find the value of the polynomial 5x – 4x2 + 3 at
x = 2
Find p(0), p(1) and p(2) for the following polynomials:-
p(y) = y2 – y + 1
Find p(0), p(1) and p(2) for the following polynomials:-
p(t) = 2 + t + 2t2 – t3
Find p(0), p(1) and p(2) for the following polynomials:-
p(x) = x3
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) = x2 – 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) = x2, 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 Class 9 Maths Chapter 2 Polynomials Exercise 2.3 [Page 40]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x+1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Check whether 7 + 3x is a factor of 3x3 + 7x.
NCERT solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.4 [Pages 43 - 44]
Determine if the following polynomial has (x + 1) a factor :-
x3 + x2 + x + 1
Determine if the following polynomial has (x + 1) a factor :-
x4 + x3 + x2 + x + 1
Determine which of the following polynomials has (x + 1) a factor :-
x4 + 3x3 + 3x2 + 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) = 2x3 + x2 – 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) = x3 + 3x2 + 3x + 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) = x3 − 4x2 + 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) = x2 + 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) = kx2 – 3x + k
Factorise :- 12x2 – 7x + 1
Factorise :- 2x2 + 7x + 3
Factorise :- 6x2 + 5x – 6
Factorise :- 3x2 – x – 4
Factorise :- x3 – 2x2 – x + 2
Factorise :- x3 – 3x2 – 9x – 5
Factorise :- x3 + 13x2 + 32x + 20
Factorise :- 2y3 + y2 – 2y – 1
NCERT solutions for Class 9 Maths 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:- 9x2 + 6xy + y2
Factorise the following using appropriate identities:- 4y2 – 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:- 4x2 + 9y2 + 16z2 + 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 :- 8a3 + b3 + 12a2b + 6ab2
Factorise :- 8a3 – b3 – 12a2b + 6ab2
Factorise :- 27 – 125a3 – 135a + 225a2
Factorise :- 64a3 – 27b3 – 144a2b + 108ab2
Factorise :-
`27p^3-1/216-9/2p^2+1/4p`
Verify :- x3 + y3 = (x + y) (x2 – xy + y2)
Verify :- x3 – y3 = (x – y) (x2 + xy + y2)
Factorise :- 27y3 + 125z3
Factorise :- 64m3 – 343n3
Factorise :- 27x3 + y3 + z3 – 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 x3 + y3 + z3 = 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 : 25a2 – 35a + 12 |
Give possible expressions for the length and breadth of the following rectangle, in which their areas are given:-
| Area : 35y2 + 13y –12 |
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
| Volume : 3x2 – 12x |
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
| Volume : 12ky2 + 8ky – 20k |
Chapter 2: Polynomials
NCERT solutions for Class 9 Maths chapter 2 - Polynomials
NCERT solutions for Class 9 Maths chapter 2 (Polynomials) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 9 Maths solutions in a manner that help students grasp basic concepts better and faster.
Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.
Concepts covered in Class 9 Maths chapter 2 Polynomials are Algebraic Identities, Factorisation of Polynomials, Concept of Polynomials, Polynomials in One Variable, Zeroes of a Polynomial, Remainder Theorem, Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0., Algebraic Identities.
Using NCERT Class 9 solutions Polynomials exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer NCERT Textbook Solutions to score more in exam.
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