NCERT Solutions For Class 9 Math | Exercise 2.1

Chapter 2 | Polynomials | 5 Questions

Detailed solution to all exercise questions of NCERT book for CBSE Class 9 Math in Chapter 2 - Polynomials - Exercise 2.1. The exercise comprises 5 questions.

Key concepts covered in this exercise include polynomials in one variable, coefficients of terms in a polynomial, classification of polynomials as monomial, binomial, and classification of polynomials as linear, quadratic, and cubic polynomials.

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 + 1
(ii) y2 + √2
(iii) 3√t + t√2
(iv) y + $$frac{2}{y}$$v) x10 + y3 + t50

Solution

(i) 4x2 - 3x + 1
It is a polynomial in one variable.
There is only one variable x and all the exponents are whole numbers.

(ii) y2 + √2
It is a polynomial in one variable.
There is only one variable y and its power is a whole number.

(iii) 3√t + t√2
It is NOT a polynomial in one variable.
The exponent of ‘t’ in √t is $$frac{1}{2}$ which is not a whole number.$iv) y + $$frac{2}{y}$ It is NOT a polynomial in one variable. The exponent of y in $\frac{2}{y}$ is -1, which is not a whole number.$v) x10 + y3 + t50
It is NOT a polynomial in one variable.
There are multiple variables involved i.e., x, y, and t

2. Question 2

Write the coefficients of x2 in each of the following :
(i) 2 + x2 + x
(ii) 2 - x2 + x3
(iii) $$frac{π}{2}$x2 + x$iv) √2x - 1

Solution

(i) 2 + x2 + x
The coefficient of x2 is 1.

(ii) 2 - x2 + x3
The coefficient of x2 is -1.

(iii) $$frac{π}{2}$x2 + x The coefficient of x2 is $\frac{π}{2}$.$iv) √2x - 1
The coefficient of x2 is 0.

3. Question 3

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

Binomial of degree 35 :- P(x) = x35 + x34

Monomial of degree 100 :- Q(y) = y100

4. 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) 5x3 + 4x2 + 7x
The highest power of x in the polynomial is 3.
The degree of the polynomial is 3.

(ii) 4 – y2
The highest power of y in the polynomial is 2.
The degree of the polynomial is 2.

(iii) 5t - √7
The highest power of t in the polynomial is 1.
The degree of the polynomial is 1.

(iv) 3
There is no variable in the polynomial.
The degree of the polynomial is 0.

5. 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) x2 + x
The highest power of x in the polynomial is 2.
Therefore the following polynomial is quadratic.

(ii) x – x3
The highest power of x in the polynomial is 3.
Therefore the following polynomial is cubic.

(iii) y + y2 + 4
The highest power of y in the polynomial is 2.
Therefore the following polynomial is quadratic.

(iv) 1 + x
The highest power of x in the polynomial is 1.
Therefore the following polynomial is linear.

(v) 3t
The highest power of t in the polynomial is 1.
Therefore the following polynomial is linear.

(vi) r2
The highest power of r in the polynomial is 2.
Therefore the following polynomial is quadratic.

(vii) 7x3
The highest power of x in the polynomial is 3.
Therefore the following polynomial is cubic.

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