NCERT Solutions Class 9 Maths Chapter 2 Polynomials Exercise 2.1 are provided here. These NCERT maths solutions are prepared by our subject experts which makes it easy for students to learn. The students use it for reference while solving the exercise problems. The first exercise in Polynomials- Exercise 2.1 discusses Polynomials in one or more variable. They provide detailed and stepwise explanations of each answer to the questions given in the exercises in the NCERT textbook for class 9. The solutions are always prepared by following NCERT guidelines so that it should cover the whole syllabus accordingly. These are very helpful in scoring well in examinations.

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**1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.**

**(i) 4x ^{2}â€“3x+7**

Solution:

The equation 4x^{2}â€“3x+7 can be written as 4x^{2}â€“3x^{1}+7x^{0}

Since *x* is the only variable in the given equation and the powers of x (i.e., 2, 1 and 0) are whole numbers, we can say that the expression 4x^{2}â€“3x+7 is a polynomial in one variable.

**(ii) y ^{2}+âˆš2**

Solution:

The equation y^{2}+**âˆš2** can be written as y^{2}+**âˆš**2y^{0}

Since y is the only variable in the given equation and the powers of y (i.e., 2 and 0) are whole numbers, we can say that the expression y^{2}+**âˆš**2 is a polynomial in one variable.

**(iii) 3âˆšt+tâˆš2 **

Solution:

The equation 3âˆšt+tâˆš2 can be written as 3t^{1/2}+âˆš2t

Though, *t* is the only variable in the given equation, the powers of *t* (i.e.,1/2) is not a whole number. Hence, we can say that the expression 3âˆšt+tâˆš2 is **not **a polynomial in one variable.

**(iv) y+2/y **

Solution:

The equation y+2/y an be written as y+2y^{-1}

Though, *y *is the only variable in the given equation, the powers of *y* (i.e.,-1) is not a whole number. Hence, we can say that the expression y+2/y is **not **a polynomial in one variable.

**(v) x ^{10}+y^{3}+t^{50}**

Solution:

Here, in the equation x^{10}+y^{3}+t^{50}

Though, the powers, 10, 3, 50, are whole numbers, there are 3 variables used in the expression

x^{10}+y^{3}+t^{50}. Hence, it is **not **a polynomial in one variable.

**2. Write the coefficients of x ^{2} in each of the following:**

**(i) 2+x ^{2}+x**

Solution:

The equation 2+x^{2}+x can be written as 2+(1)x^{2}+x

We know that, coefficient is the number which multiplies the variable.

Here, the number that multiplies the variable x^{2} is 1

, the coefficients of x^{2 }in 2+x^{2}+x is 1.

**(ii) 2â€“x ^{2}+x^{3}**

Solution:

The equation 2â€“x^{2}+x^{3 }can be written as 2+(â€“1)x^{2}+x^{3}

We know that, coefficient is the number (along with its sign, i.e., â€“ or +) which multiplies the variable.

Here, the number that multiplies the variable x^{2} is -1

the coefficients of x^{2 }in 2â€“x^{2}+x^{3 }is -1.

**(iii) (/2)x ^{2}+x**

Solution:

The equation (/2)x^{2 }+x can be written as (/2)x^{2} + x

We know that, coefficient is the number (along with its sign, i.e., â€“ or +) which multiplies the variable.

Here, the number that multiplies the variable x^{2} is /2.

the coefficients of x^{2 }in (/2)x^{2 }+x is /2.

**(iii)âˆš2x-1**

Solution:

The equation âˆš2x-1 can be written as 0x^{2}+âˆš2x-1 [Since 0x^{2} is 0]

We know that, coefficient is the number (along with its sign, i.e., â€“ or +) which multiplies the variable.

Here, the number that multiplies the variable x^{2}is 0

, the coefficients of x^{2 }in âˆš2x-1 is 0.

**3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.**

Solution:

Binomial of degree 35: A polynomial having two terms and the highest degree 35 is called a binomial of degree 35

Eg., Â 3x^{35}+5

Monomial of degree 100: A polynomial having one term and the highest degree 100 is called a monomial of degree 100

Eg., Â 4x^{100}

**4. Write the degree of each of the following polynomials:**

**(i) 5x ^{3}+4x^{2}+7x**

Solution:

The highest power of the variable in a polynomial is the degree of the polynomial.

Here, 5x^{3}+4x^{2}+7x = 5x^{3}+4x^{2}+7x^{1}

The powers of the variable x are: 3, 2, 1

the degree of 5x^{3}+4x^{2}+7x is 3 as 3 is the highest power of x in the equation.

**(ii) 4â€“y ^{2}**

Solution:

The highest power of the variable in a polynomial is the degree of the polynomial.

Here, in 4â€“y^{2},

The power of the variable y is 2

the degree of 4â€“y^{2} is 2 as 2 is the highest power of y in the equation.

**(iii) 5tâ€“âˆš7 **

Solution:

The highest power of the variable in a polynomial is the degree of the polynomial.

Here, in 5t**â€“âˆš7 ,**

The power of the variable t is: 1

the degree of 5t**â€“âˆš7 **is 1 as 1 is the highest power of y in the equation.

**(iv) 3**

Solution:

The highest power of the variable in a polynomial is the degree of the polynomial.

Here, 3 = 3Ã—1 = 3Ã— x^{0}

The power of the variable here is: 0

the degree of 3 is 0.

**5. Classify the following as linear, quadratic and cubic polynomials:**

Solution:

We know that,

Linear polynomial: A polynomial of degree one is called a linear polynomial.

Quadratic polynomial: A polynomial of degree two is called a quadratic polynomial.

Cubic polynomial: A polynomial of degree three is called a cubic polynomial.

**(i) x ^{2}+x**

Solution:

The highest power of x^{2}+x is 2

the degree is 2

Hence, x^{2}+x is a quadratic polynomial

**(ii) xâ€“x ^{3}**

Solution:

The highest power of xâ€“x^{3 }is 3

the degree is 3

Hence, xâ€“x^{3} is a cubic polynomial

**(iii) y+y ^{2}+4**

Solution:

The highest power of y+y^{2}+4 is 2

the degree is 2

Hence, y+y^{2}+4is a quadratic polynomial

**(iv) 1+x**

Solution:

The highest power of 1+x is 1

the degree is 1

Hence, 1+x is a linear polynomial.

**(v) 3t**

Solution:

The highest power of 3t is 1

the degree is 1

Hence, 3t is a linear polynomial.

**(vi) r ^{2}**

Solution:

The highest power of r^{2 }is 2

the degree is 2

Hence, r^{2}is a quadratic polynomial.

**(vii) 7x ^{3}**

Solution:

The highest power of 7x^{3 }is 3

the degree is 3

Hence, 7x^{3} is a cubic polynomial.

### Access other exercise solutions of Class 9 Maths Chapter 2- Polynomials

Exercise 2.2 Solutions 4 Questions

Exercise 2.3 Solutions 3 Questions

Exercise 2.4 Solutions 5 Questions

Exercise 2.5 Solutions 16 Questions

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

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