These NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 Questions and Answers are prepared by our highly skilled subject experts.

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

Question 1.

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

(i) 4x^{2} – 3x + 7

(ii) y^{2} + √2

(iii) 3√t + t√2

(iv) y + \(\frac{2}{y}\)

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

Solution:

(i) Yes, 4x^{2} – 3x + 7 is polynomial of one variable. As x has degree 2 in it and the only x is one variable.

(ii) Yes, y is only one variable.

(iii) No as 3√t + t√2 can be written as \(3 t^{\frac{1}{2}}+t \sqrt{2}\), Here the exponent of t in \(3 t^{\frac{1}{2}}\) is \(\frac {1}{2}\) which is not a whole number.

(iv) No, as y + \(\frac{2}{y}\) can be written as y + 2y^{-1} where exponent of y in \(\frac{2}{y}\) is -1, which is not a whole number.

(v) Yes, it is a polynomial in three variables x, y, and 1.

Question 2.

Write the co-efficients of x^{2} in each of the following:

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

(ii) 2 – x^{2} + x^{3}

(iii) \(\frac{\pi}{2} x^{2}+x\)

(iv) \(\sqrt{2 x}-1\)

Solution:

(i) We have given that the equation 2 + x^{2} + x

we can also write 1x^{2} + 1x + 2

Therefore, the coefficient of x^{2} in this equation is 1.

(ii) we have given that the equation:

2 – x^{2} + x^{3}

we can also write

x^{3} – 1x^{2} + 2

Therefore, the coefficient of x^{2} in this equation is -1.

(iii) We have given that the equation

\(\frac{\pi}{2} x^{2}+x\)

or, \(\frac{\frac{22}{7} x^{2}+1 x}{2}\) (since π = \(\frac {22}{7}\))

or, \(\frac{22}{7 \times 2} x^{2}+1 x\)

or, \(\frac{11}{7} x^{2}+1 x\)

Therefore, the coefficient of x^{2} in this equation is \(\frac{11}{7}\).

(iv) We have given that the equation √2x – 1.

We can also write 0x^{2} + √2x – 1

Therefore, the coefficient of x^{2} in this equation is 0.

Question 3.

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

Solution:

We know that polynomials having only two terms is called binomial.

Therefore, the example of a binomial of degree 35 is ax^{35} + b where a and b are any real number.

Again, the example of a monomial of degree 100 is ax^{100} where a is any real number.

Question 4.

Write the degree of each of the following polynomials:

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

(ii) 4 – y^{2}

(iii) 5t – √7

(iv) 3

Solution:

(i) We know that the highest power of the variable in a polynomial is called the degree of the polynomial.

In polynomial 5x^{3} + 4x^{2} + 7x.

The highest power of variable x is 3.

Therefore, the degree of polynomial 5x^{3} + 4x^{2} + 7x is 3.

(ii) In polynomial 4 – y^{2}, the highest power of the variable y is 2.

Therefore, the degree of the polynomial 4 – y^{2} is 2.

(iii) In polynomial 5t – 5, the highest power of the variable t is 1.

Therefore, the degree of polynomial 5t – 5 is 1.

(iv) The only term here is 3 which can be written as 3x^{0}: So the highest power of the variable x is 0.

Therefore, the degree of the polynomial 3 is 0.

Question 5.

Classify the following as linear, quadratic and cubic polynomials

(i) x^{2} + x

(ii) x – x^{3}

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

(iv) 1 + x

(v) 3t

(vi) r^{2}

(vii) 7x^{3}

Solution:

(i) In polynomial x^{2} + x the highest power of the variable x is 2. So the degree of the polynomial is 2.

We know that the polynomial of degree 2 is called a quadratic polynomial.

Therefore, polynomial x^{2} + x is a quadratic polynomial.

(ii) In polynomial x – x^{3}, the highest power of the variable x is 3. So the degree of the polynomial is 3.

We know that the polynomial of degree 3 is called a cubic polynomial.

Therefore, polynomial x – x^{3} is a cubic polynomial.

(iii) In polynomial y + y^{2} + 4, the highest power of the variable y is 2. So the degree of the polynomial is 2.

We know that the polynomial of degree 2 is called a quadratic polynomial.

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

(iv) In polynomial 1 + x, the highest power of the variable x is 1. So the degree of the polynomial is 1.

We know that the polynomial of degree 1 is called a linear polynomial.

Therefore, polynomial 1 + x is a linear polynomial.

(v) In polynomial 3t, the highest power of the variable t is 1. So, the degree of the polynomial is 1.

We know that the polynomial of degree 1 is called a linear polynomial.

Therefore, polynomial 3t is a linear polynomial.

(vi) In polynomial r^{2}, the highest power of the variable r is 2. So, the degree of the polynomial is 2.

We know that the polynomial of degree 2 is called a quadratic polynomial.

Therefore, polynomial r is a quadratic polynomial.

(vii) In polynomial 7x^{3}, the highest power of the variable x is 3. So the degree of the polynomial is 3.

We know that the polynomial of degree 3 is called a cubic polynomial.

Therefore polynomial 7x^{3} is a cubic polynomial.