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# NCERT Solution - Polynomials Class 9 Notes | EduRev

## Class 9 : NCERT Solution - Polynomials Class 9 Notes | EduRev

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Class IX  Chapter 2 Polynomials
Maths

Exercise 2.1 Question
1:
Which of the following expressions are polynomials in one variable and which are

No. It can be observed that the exponent of variable t in term is  , which is
not a whole number. Therefore, this expression is not a polynomial.
(iv)

Page 2

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Class IX  Chapter 2 Polynomials
Maths

Exercise 2.1 Question
1:
Which of the following expressions are polynomials in one variable and which are

No. It can be observed that the exponent of variable t in term is  , which is
not a whole number. Therefore, this expression is not a polynomial.
(iv)

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No. It can be observed that the exponent of variable y in term is -1, which is not a
whole number. Therefore, this expression is not a polynomial.
(v)
No. It can be observed that this expression is a polynomial in 3 variables x, y, and t.
Therefore, it is not a polynomial in one variable.

In the above expression, the coefficient of is -1.
(iii)
In the above expression, the coefficient of

In the above expression, the coefficient of is 0.
Question 3:
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Degree of a polynomial is the highest power of the variable in the polynomial.
Binomial has two terms in it. Therefore, binomial of degree 35 can be written as
.
Monomial has only one term in it. Therefore, monomial of degree 100 can be written
as x
100
.
Question 2:
Write the coefficients of  in each of the following:

In the above expression, the coefficient of  is 1.
( ii )

(   i)    (   ii)
(   iii)    (   iv)
( i)
.    is

(   iv)

Page 3

Cbse-spot.blogspot.com

Class IX  Chapter 2 Polynomials
Maths

Exercise 2.1 Question
1:
Which of the following expressions are polynomials in one variable and which are

No. It can be observed that the exponent of variable t in term is  , which is
not a whole number. Therefore, this expression is not a polynomial.
(iv)

Cbse-spot.blogspot.com
No. It can be observed that the exponent of variable y in term is -1, which is not a
whole number. Therefore, this expression is not a polynomial.
(v)
No. It can be observed that this expression is a polynomial in 3 variables x, y, and t.
Therefore, it is not a polynomial in one variable.

In the above expression, the coefficient of is -1.
(iii)
In the above expression, the coefficient of

In the above expression, the coefficient of is 0.
Question 3:
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Degree of a polynomial is the highest power of the variable in the polynomial.
Binomial has two terms in it. Therefore, binomial of degree 35 can be written as
.
Monomial has only one term in it. Therefore, monomial of degree 100 can be written
as x
100
.
Question 2:
Write the coefficients of  in each of the following:

In the above expression, the coefficient of  is 1.
( ii )

(   i)    (   ii)
(   iii)    (   iv)
( i)
.    is

(   iv)

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Question 4:
Write the degree of each of the following polynomials:

Degree of a polynomial is the highest power of the variable in the polynomial.
(i)
This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the
degree of this polynomial is 3.
(ii)
This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the
degree of this polynomial is 2.
(iii)
This is a polynomial in variable t and the highest power of variable t is 1. Therefore,
the degree of this polynomial is 1.
(iv) 3

This is a constant polynomial. Degree of a constant polynomial is always 0.
Question 5:
Classify the following as linear, quadratic and cubic polynomial:
(i)
(vi)
( i)
( iii)
(   ii)
(   iv) 3
ii)  (   (   iii)    (   iv)    (   v)
(   vii)
Page 4

Cbse-spot.blogspot.com

Class IX  Chapter 2 Polynomials
Maths

Exercise 2.1 Question
1:
Which of the following expressions are polynomials in one variable and which are

No. It can be observed that the exponent of variable t in term is  , which is
not a whole number. Therefore, this expression is not a polynomial.
(iv)

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No. It can be observed that the exponent of variable y in term is -1, which is not a
whole number. Therefore, this expression is not a polynomial.
(v)
No. It can be observed that this expression is a polynomial in 3 variables x, y, and t.
Therefore, it is not a polynomial in one variable.

In the above expression, the coefficient of is -1.
(iii)
In the above expression, the coefficient of

In the above expression, the coefficient of is 0.
Question 3:
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Degree of a polynomial is the highest power of the variable in the polynomial.
Binomial has two terms in it. Therefore, binomial of degree 35 can be written as
.
Monomial has only one term in it. Therefore, monomial of degree 100 can be written
as x
100
.
Question 2:
Write the coefficients of  in each of the following:

In the above expression, the coefficient of  is 1.
( ii )

(   i)    (   ii)
(   iii)    (   iv)
( i)
.    is

(   iv)

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Question 4:
Write the degree of each of the following polynomials:

Degree of a polynomial is the highest power of the variable in the polynomial.
(i)
This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the
degree of this polynomial is 3.
(ii)
This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the
degree of this polynomial is 2.
(iii)
This is a polynomial in variable t and the highest power of variable t is 1. Therefore,
the degree of this polynomial is 1.
(iv) 3

This is a constant polynomial. Degree of a constant polynomial is always 0.
Question 5:
Classify the following as linear, quadratic and cubic polynomial:
(i)
(vi)
( i)
( iii)
(   ii)
(   iv) 3
ii)  (   (   iii)    (   iv)    (   v)
(   vii)

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Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1,
2, and 3 respectively.
as its degree is 2.
(ii) is a cubic polynomial as
its degree is 3.  (iii)  is a quadratic polynomial
as its degree is 2.
(iv) 1 + x is a linear polynomial as its degree is 1.
(v) is a linear polynomial as its degree is 1.
(vi) is a quadratic polynomial as its degree is 2.
(vii) is a cubic polynomial as its degree is 3.

Page 5

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Class IX  Chapter 2 Polynomials
Maths

Exercise 2.1 Question
1:
Which of the following expressions are polynomials in one variable and which are

No. It can be observed that the exponent of variable t in term is  , which is
not a whole number. Therefore, this expression is not a polynomial.
(iv)

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No. It can be observed that the exponent of variable y in term is -1, which is not a
whole number. Therefore, this expression is not a polynomial.
(v)
No. It can be observed that this expression is a polynomial in 3 variables x, y, and t.
Therefore, it is not a polynomial in one variable.

In the above expression, the coefficient of is -1.
(iii)
In the above expression, the coefficient of

In the above expression, the coefficient of is 0.
Question 3:
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Degree of a polynomial is the highest power of the variable in the polynomial.
Binomial has two terms in it. Therefore, binomial of degree 35 can be written as
.
Monomial has only one term in it. Therefore, monomial of degree 100 can be written
as x
100
.
Question 2:
Write the coefficients of  in each of the following:

In the above expression, the coefficient of  is 1.
( ii )

(   i)    (   ii)
(   iii)    (   iv)
( i)
.    is

(   iv)

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Question 4:
Write the degree of each of the following polynomials:

Degree of a polynomial is the highest power of the variable in the polynomial.
(i)
This is a polynomial in variable x and the highest power of variable x is 3. Therefore, the
degree of this polynomial is 3.
(ii)
This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the
degree of this polynomial is 2.
(iii)
This is a polynomial in variable t and the highest power of variable t is 1. Therefore,
the degree of this polynomial is 1.
(iv) 3

This is a constant polynomial. Degree of a constant polynomial is always 0.
Question 5:
Classify the following as linear, quadratic and cubic polynomial:
(i)
(vi)
( i)
( iii)
(   ii)
(   iv) 3
ii)  (   (   iii)    (   iv)    (   v)
(   vii)

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Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1,
2, and 3 respectively.
as its degree is 2.
(ii) is a cubic polynomial as
its degree is 3.  (iii)  is a quadratic polynomial
as its degree is 2.
(iv) 1 + x is a linear polynomial as its degree is 1.
(v) is a linear polynomial as its degree is 1.
(vi) is a quadratic polynomial as its degree is 2.
(vii) is a cubic polynomial as its degree is 3.

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Exercise 2.2 Question
1:
Find the value of the polynomial at
(i) x = 0 (ii) x = -1 (iii) x = 2

Find p(0), p(1) and p(2) for each of the following polynomials:
(i) p(y) = y
2
- y + 1 (ii) p(t) = 2 + t + 2t
2
- t
3

(iii) p(x) = x
3
(iv) p(x) = (x - 1) (x + 1)
2
- y + 1 p(0) =
(0)
2
- (0) + 1 = 1 p(1) = (1)
2
- (1) + 1 =
1 p(2) = (2)
2
- (2) + 1 = 3 (ii) p(t) =
2 + t + 2t
2
- t
3
p(0) = 2 + 0 + 2 (0)
2
-

( i)

(   ii)

(   iii)

Question 2:
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