NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1.

• NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.1
• NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.2
• NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.3
• NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.4
• NCERT Solutions for Class 9 Maths Chapter 2 Number Systems Ex 2.5

Ex 2.1 Class 9 Maths Question 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x² – 3x + 7              (ii) y² + √2               (iii) 3√t + t√2
(iv) y + 2/y                    (v) x¹⁰ + y³ + t⁵⁰

Solution:
(i) 4x² – 3x + 7

It is a polynomial in one variable, i.e., x, because each exponent of x is a whole number.

(ii) y² + √2
It is a polynomial in one variable, i.e., y, because each exponent of y is a whole number.

(iii) 3√t + t√2 = 3(t)^1/2 + √2.t
It is not a polynomial, because one of the exponents of t is 1/2, which is not a whole number.

(iv) y + 2/y = y + 2.y^-1
It is not a polynomial, because one of the exponents of y is -1, which is not a whole number.

(v) x¹⁰ + y³ + t⁵⁰
Here, exponent of every variable is a whole number, but x¹⁰ + y³ + t⁵⁰ is a polynomial in three variables, i.e., in x, y and t.
So, it is not a polynomial in one variable.

 

Ex 2.1 Class 9 Maths Question 2.
Write the coefficients of x² in each of the following:
(i) 2 + x² + x                            (ii) 2 – x² + x³
(iii) π/2 . x² + x                       (iv) √2 x – 1

Solution:
(i) The given polynomial is 2 + x² + x.
The coefficient of x² is 1.
(ii) The given polynomial is 2 – x² + x³.
The coefficient of x² is -1.
(iii) The given polynomial is π/2 . x² + x.
The coefficient of x² is π/2.
(iv) The given polynomial is √2 x – 1. It can be written as 0.x² + √2 x – 1.
The coefficient of x² is 0.

 

Ex 2.1 Class 9 Maths Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Solution:
(i) A binomial of degree 35 can be written as 2x³⁵ + 5.
(ii) A monomial of degree 100 can be written as 4y¹⁰⁰ – 3.

 

Ex 2.1 Class 9 Maths Question 4.
Write the degree of each of the following polynomials.
(i) 5x³ + 4x² + 7x                       (ii) 4 – y²
(iii) 5t – √7                                (iv) 3

Solution:
(i) The given polynomial is 5x³ + 4x² + 7x.
The highest power of the variable x is 3.
So, the degree of the polynomial is 3.
(ii) The given polynomial is 4 – y².

The highest power of the variable y is 2.
So, the degree of the polynomial is 2.
(iii) The given polynomial is 5t – √7.

The highest power of the variable t is 1.

So, the degree of the polynomial is 1.
(iv) The given polynomial is 3.

Since, 3 can be written as 3x⁰. That is 3 = 3x⁰      [∵ x⁰ = 1]
So, the degree of the polynomial is 0.

 

Ex 2.1 Class 9 Maths Question 5.
Classify the following as linear, quadratic and cubic polynomials:
(i) x² + x                                    (ii) x – x³                             (iii) y + y²+ 4                                    (iv) 1 + x                                   (v) 3t                                 (vi) r²
(vii) 7x³

Solution:
(i) The highest degree of x² + x is 2. So, it is a quadratic polynomial.
(ii) The highest degree of x – x³ is 3. So, it is a cubic polynomial.

(iii) The highest degree of y + y² + 4 is 2. So, it is a quadratic polynomial.

(iv) The highest degree of 1 + x is 1. So, it is a linear polynomial.
(v) The highest degree of 3t is 1. So, it is a linear polynomial.
(vi) The highest degree of r² is 2. So, it is a quadratic polynomial.
(vii) The highest degree of 7x³ is 3. So, it is a cubic polynomial.

 

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