NCERT Solutions Class 9 Chapter 2 Polynomials Exercise 2.1

Polynomials Class 9 Exercise 2.1 introduces you to the basic structure of polynomials, including terms, coefficients, variables, and degrees. It helps students understand how algebraic expressions are formed and how they behave in equations.

The NCERT Solutions provided here break down each problem using simple explanations so that you can understand how to classify and identify polynomials. 

Class 9 Chapter 2 Polynomials Exercise 2.1 Questions

The Class 9 Chapter 2 Polynomials Exercise 2.1 questions focus on identifying algebraic expressions as polynomials, determining their degree, listing coefficients, and recognizing different types such as linear, quadratic, and cubic polynomials. Below are the NCERT Solutions Class 9 Chapter 2 Ex 2.1:

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

Solution: The equation 4x 2 –3x+7 can be written as 4x 2 –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 –3x+7 is a polynomial in one variable.

(ii) y 2 +√2

Solution: The equation y 2 + √2 can be written as y 2 + √ 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 + √ 2 is a polynomial in one variable.

(iii) 3√t+t√2

Solution: The equation 3√t+t√2 can be written as 3t 1/2 +√2t Though t is the only variable in the given equation, the power of t (i.e., 1/2) is not a whole number. Hence, we can say that the expression 3√t+t√2 is not a polynomial in one variable.

(iv) y+2/y

Solution: The equation y+2/y can be written as y+2y -1 Though y is the only variable in the given equation, the power 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 the coefficient is the number which multiplies the variable. Here, the number that multiplies the variable x 2 is 1 Hence, the coefficient of x 2 in 2+x 2 +x is 1.

(ii) 2–x 2 +x 3

Solution: The equation 2–x 2 +x 3 can be written as 2+(–1)x 2 +x 3 We know that the coefficient is the number (along with its sign, i.e. – or +) which multiplies the variable. Here, the number that multiplies the variable x 2 is -1 Hence, the coefficient of x 2 in 2–x 2 +x 3 is -1.

(iii) ( π /2)x 2 +x

Solution: The equation (π/2)x 2 +x can be written as (π/2)x 2 + x We know that the coefficient is the number (along with its sign, i.e. – or +) which multiplies the variable. Here, the number that multiplies the variable x 2 is π/2. Hence, the coefficient of x 2 in (π/2)x 2 +x is π/2.

(iii)√2x-1

Solution: The equation √2x-1 can be written as 0x 2 +√2x-1 [Since 0x 2 is 0] We know that the coefficient is the number (along with its sign, i.e. – or +) which multiplies the variable. Here, the number that multiplies the variable x 2 is 0 Hence, the coefficient of x 2 in √2x-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. For example,  3x 35 +5 Monomial of degree 100: A polynomial having one term and the highest degree 100 is called a monomial of degree 100. For example,  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) 4–y 2

Solution: The highest power of the variable in a polynomial is the degree of the polynomial. Here, in 4–y 2 , The power of the variable y is 2 The degree of 4–y 2 is 2, as 2 is the highest power of y in the equation.

(iii) 5t–√7

Solution: The highest power of the variable in a polynomial is the degree of the polynomial. Here, in 5t –√7 The power of the variable t is: 1 The degree of 5t –√7 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 = 3×1 = 3× x 0 The power of the variable here is: 0 Hence, 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) x–x 3

Solution: The highest power of x–x 3 is 3 The degree is 3 Hence, x–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 +4 is 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.

NCERT Maths Class 9 Polynomials Exercise 2.1 PDF

NCERT Maths Class 9 Polynomials Exercise 2.1 PDF provides well-structured solutions that explain every question step by step. You can use this PDF to revise important concepts like coefficients, degrees, and types of polynomials in a quick and organized manner. It is especially useful for self-study and exam preparation.

It will help you understand the fundamentals of Chapter 2 Polynomials Class 9. It simplifies difficult definitions and provides clear examples so you can strengthen your conceptual understanding and improve accuracy in exams.

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