NCERT Solution - Polynomials Class 9 Notes | EduRev

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

 Page 1


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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.   
Answer:   
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)        
Answer:    
  ( i)        
.    is   
    
(   iv)    
    
Page 3


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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)    
   
   
 
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.   
Answer:   
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)        
Answer:    
  ( i)        
.    is   
    
(   iv)    
    
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Question 4:   
Write the degree of each of the following polynomials:   
 
Answer:   
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


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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)    
   
   
 
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.   
Answer:   
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)        
Answer:    
  ( i)        
.    is   
    
(   iv)    
    
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Question 4:   
Write the degree of each of the following polynomials:   
 
Answer:   
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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Answer:   
Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 
2, and 3 respectively.   
(i) is a quadratic polynomial 
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)    
   
   
 
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.   
Answer:   
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)        
Answer:    
  ( i)        
.    is   
    
(   iv)    
    
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Question 4:   
Write the degree of each of the following polynomials:   
 
Answer:   
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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Answer:   
Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 
2, and 3 respectively.   
(i) is a quadratic polynomial 
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)  
Answer:  (i) p(y) = y
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
 -  
  
Answer:    
  ( i)        
    
(   ii)        
    
(   iii)        
    
Question 2:    
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