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

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) 4x2 – 3x + 7
(ii) y2 + √2
(iii) 3√t + t√2
(iv) y + $$\frac{2}{y}$$
(v) x10 + y3 + t50
Solution:
(i) Yes, 4x2 – 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 x2 in each of the following:
(i) 2 + x2 + x
(ii) 2 – x2 + x3
(iii) $$\frac{\pi}{2} x^{2}+x$$
(iv) $$\sqrt{2 x}-1$$
Solution:
(i) We have given that the equation 2 + x2 + x
we can also write 1x2 + 1x + 2
Therefore, the coefficient of x2 in this equation is 1.

(ii) we have given that the equation:
2 – x2 + x3
we can also write
x3 – 1x2 + 2
Therefore, the coefficient of x2 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 x2 in this equation is $$\frac{11}{7}$$.

(iv) We have given that the equation √2x – 1.
We can also write 0x2 + √2x – 1
Therefore, the coefficient of x2 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 ax35 + b where a and b are any real number.
Again, the example of a monomial of degree 100 is ax100 where a is any real number.

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) We know that the highest power of the variable in a polynomial is called the degree of the polynomial.
In polynomial 5x3 + 4x2 + 7x.
The highest power of variable x is 3.
Therefore, the degree of polynomial 5x3 + 4x2 + 7x is 3.

(ii) In polynomial 4 – y2, the highest power of the variable y is 2.
Therefore, the degree of the polynomial 4 – y2 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 3x0: 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) x2 + x
(ii) x – x3
(iii) y + y2 + 4
(iv) 1 + x
(v) 3t
(vi) r2
(vii) 7x3
Solution:
(i) In polynomial x2 + 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 x2 + x is a quadratic polynomial.

(ii) In polynomial x – x3, 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 – x3 is a cubic polynomial.

(iii) In polynomial y + y2 + 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 + y2 + 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 r2, 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 7x3, 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 7x3 is a cubic polynomial.

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