# Ex 2.1 Class 9

## NCERT Solutions for Class 9 Maths Chapter-2 Polynomials Exercise 2.1

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+ 2y

(v) x10+ y3+t50

Sol. (i) We can write the equation 4x2 – 3x + 7 as

= 4x2 – 3x + 7x0

Since, x is the only variable in this equation,

It is a polynomial in one variable i.e., x

because each exponent of x is a whole number.

(ii) We have y2 + √2 = y2 + √2y0

Since, y is the only variable in this equation,

It is a polynomial in one variable i.e., y

because each exponent of y is a whole number.

(iii) We have 3√t + t√2 = 3t1/2 + √2t

because t is the only variable in this equation,

It is not a polynomial, because one of the exponents of t is 1/2,

which is not a whole number.

(iv) We have  y+2y=y+2y-1

As we can see, y is the only variable in this equation,

It is not a polynomial, because one of the exponents of y is -1,

which is not a whole number.

(v) We have x10+  y3 + t50

Here, the exponent of every variable is a whole number, but x10+  y3 + t50 is a polynomial in x, y and t, i.e., in three variables.

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

(iv) √2 x – 1

Sol. (i) The given polynomial is 2 + x2 + x

It can be written as, 2 + (1)x2 + x

The coefficient of x2 is 1.

(ii) The given polynomial is 2 – x2 + x3

It can be written as, 2 – (1)x2 + x3

The coefficient of x2 is -1.

(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.

Sol. (i) A binomial of degree 35 can be 7x35 -2.

(ii) A monomial of degree 100 can be 3y100.

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

Sol.

(i) It is given that, 5x3 + 4x2 + 7x.

The highest power of the variable x is 3.

So, the degree of the polynomial is 3.

(ii) In polynomial 4 – y2

The highest power of the variable y is 2.

So, the degree of the polynomial is 2.

(iii) In the given polynomial 5t – √7.

The highest power of variable t is 1.

So, the degree of the polynomial is 1.

(iv) As we know, 3 = 3x°

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

Sol. Linear polynomial: A polynomial of degree one.

Quadratic Polynomial: A polynomial of degree two.

Cubic Polynomial: A polynomial of degree three.

(i) The degree of x2 + x is 2. So, it is a quadratic polynomial.

(ii) The degree of x – x3 is 3. So, it is a cubic polynomial.

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

(iv) The degree of 1 + x is 1. So, it is a linear polynomial.

(v) The degree of 3t is 1. So, it is a linear polynomial.

(vi) The degree of r2 is 2. So, it is a quadratic polynomial.

(vii) The degree of 7x3 is 3. So, it is a cubic polynomial.