Exercise 2.1 NCERT Class 9 Polynomials Best Math Solutions

Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.5 Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4

Exercise 2.1 NCERT Class 9 contains a total of five questions. The questions are based on the following topics.

Algebraic Expressions
Terms of an Algebraic Expression
Polynomials in one variable
Coefficient of a term in a polynomial
Degree of polynomials
Number of terms in a polynomial
Linear, quadratic and cubic polynomials

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Exercise 2.1 NCERT Class 9 Polynomials Solutions

Q.1 Q.2 Q.3 Q.4 Q.5

The first question in exercise 2.1 NCERT Class 9 is all about identifying polynomials.

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

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

Answer

$4 x^{2} - 3 x + 7$ is a polynomial as the exponents of the variable $x$ are 2 and 1 which are whole numbers.

(ii) $y^{2} + \sqrt{2}$

Answer

$y^{2} + \sqrt{2}$ is a polynomial as the exponent of the variable y is 2 which is a whole number.

(iii) $3 \sqrt{t} + t \sqrt{2}$

Answer

∵ $3 \sqrt{t} + t \sqrt{2}$ = $3 t^{\frac{1}{2}} + t \sqrt{2}$

Here, one exponent of the variable t is $\frac{1}{2}$ which is not a whole number.Therefore, the given algebraic expression is not a polynomial.

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

Answer

∵ $y + \frac{2}{y}$ = $y + 2 y^{- 1}$

Here, one power of the variable y is −1 which is not a whole number. Therefore, the given algebraic expression is not a polynomial.

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

Answer

$x^{10} + y^{3} + t^{50}$ is a polynomial as the exponents of the variables x, y and t are 10, 3 and 50 respectively. And all of these are whole numbers.

The second question of Exercise 2.1 NCERT Class 9 is about finding the coefficients of a term.

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

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

Answer

The given expression is
$2 + x^{2} + x$ = $2 + (1 \times x^{2}) + x$
Here, the coefficient of $x^{2}$ is 1.

(ii) $2 - x^{2} + x^{3}$

Answer

We have
$2 - x^{2} + x^{3}$ = $2 + (- 1) \times x^{2} + x^{3}$

Here, the coefficient of $x^{2}$ is −1

(iii) $\frac{π}{2} x^{2} + x$

Answer

The given expression is $\frac{π}{2} x^{2} + x$ .
Here, the coefficient of $x^{2}$ is $\frac{π}{2}$ .

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

Answer

We have
$\sqrt{2} x - 1$ = $0 x^{2} + \sqrt{2} x - 1$
Clearly, the coefficient of $x^{2}$ is 0.

In Exercise 2.1 NCERT Class 9, the third question asks us to find a monomial and binomial of a given degree.

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

Answer

You can give the following examples.
Binomials of degree 35
(i) $3 x^{35} - 4$
(ii) $2 x^{35} + 3 x^{34}$
(iii) $7 x^{35} + \sqrt{3} x^{12}$
(iv) etc.
Key Idea: The binomial must have one term with a power of 35 and another term with a lower power.

Monomials of degree 100
(i) $\sqrt{2} x^{100}$
(ii) $2 x^{100}$
(iii) $- 8 x^{100}$
(iv) etc.
Key Idea: The monomial must have only one term with a power of 100.

In Exercise 2.1 NCERT Class 9, the fourth question asks us to find out degree of a polynomial.

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

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

Answer

The given expression is $5 x^{3} + 4 x^{2} + 7 x$ Here, the degree is $3$ .

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

(ii) $4 - y^{2}$

Answer

The given expression is $4 - y^{2}$ .
Here, the degree is $2$ .

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

(iii) $5 t - \sqrt{7}$

Answer

The given expression is $5 t - \sqrt{7}$ .
Here, the degree is $1$ .

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

(iv) 3

Answer

We have $3$ = $3 x^{0}$ .
Here, the degree is 0.

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

In Exercise 2.1 NCERT Class 9, the fifth question asks us to classify the given polynomials into linear, quadratic and cubic polynomials:

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

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

Answer

The given expression is $x^{2} + x$ .
Since the degree of the polynomial is 2, it is a quadratic polynomial.

(ii) $x - x^{3}$

Answer

The given expression is $x - x^{3}$ . The degree of the polynomial is three, indicating that it is a cubic polynomial .

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

Answer

The given expression is $y + y^{2} + 4$ .
Since the degree of the polynomial is 2, it is a quadratic polynomial.

(iv) $1 + x$

Answer

The given polynomial is $1 + x$ .
Since the degree of the polynomial is 1, it is a linear polynomial.

(v) 3t

Answer

The given polynomial is 3t.
Since the degree of the polynomial is 1, it is a linear polynomial.

(vi) $r^{2}$

Answer

The given polynomial is $r^{2}$ .
Since the degree of the polynomial is 2, it is a quadratic polynomial.

(vii) $7 x^{3}$

Answer

The given polynomial is $7 x^{3}$ .
Since the degree of the polynomial is 3, it is a cubic polynomial.

Degree vs Polynomial's Name

Degree	Name
1	Linear
2	Quadratic
3	Cubic
4	Biquadratic or quartic
5	Quintic
6	Sextic or hexic
7	Septic or heptic
8	Octic
9	Nonic
10	Decic

Exercise 2.1 NCERT Class 9 Polynomials Solutions

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

(i) 4x2−3x+7

Answer

(ii) y2+2

Answer

(iii) 3t+t2

Answer

(iv) y+2y

Answer

(v) x10+y3+t50

Answer

2. Write the coefficients of x2 in each of the following:

(i) 2+x2+x

Answer

(ii) 2−x2+x3

Answer

(iii) π2x2+x

Answer

(iv) 2x−1

Answer

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

Answer

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

(i) 5x3+4x2+7x

Answer

(ii) 4−y2

Answer

(iii) 5t−7

Answer

(iv) 3

Answer

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

(i) x2+x

Answer

(ii) x−x3

Answer

(iii) y+y2+4

Answer

(iv) 1+x

Answer

(v) 3t

Answer

(vi) r2

Answer

(vii) 7x3

Answer

Degree vs Polynomial's Name

Important Links

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

(ii) $y^{2} + \sqrt{2}$

(iii) $3 \sqrt{t} + t \sqrt{2}$

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

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

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

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

(ii) $2 - x^{2} + x^{3}$

(iii) $\frac{π}{2} x^{2} + x$

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

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

(ii) $4 - y^{2}$

(iii) $5 t - \sqrt{7}$

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

(ii) $x - x^{3}$

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

(iv) $1 + x$

(vi) $r^{2}$

(vii) $7 x^{3}$