NCERT Solutions Class 9 Mathematics

Exercise 2.1

Q.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) 3t + t2

(iv) y + 2y (v) x10 + y3 + t50

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

  1. 2 + x2 + x

  2. 2 - x2 + x3

  3. π2 x2 + x

  4. 2x - 1

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

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

  1. 5x3 + 4x2 + 7x

  2. 4 - y2

  3. 5t - 7

  4. 3

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

  1. x2 + x
  1. x - x3
  1. y + y2 +4
  1. 1 + x
  1. t
  1. r2
  1. 7x3

NCERT Solutions Class 9 Mathematics

Exercise 2.1

Q.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) 3t + t2

(iv) y + 2y (v) x10 + y3 + t50

Solution:

  1. 4x2 - 3x + 7: This is an expression with only one variable x with +ve integer powers. Hence, this is a polynomial in one variable.

  2. y2 + 2: This is an expression with only one variable y with +ve integer powers. Hence, this is a polynomial in one variable.

  3. 3t + t2: This is an expression with only one variable t but one of the powers of t is 12 (in 3t), which is not +ve integer. Hence, this is not a polynomial.

  4. y + 2y = y + 2y-1: This is an expression with only one variable y but one of the powers of y is -1, which is not +ve integer. Hence, this is not a polynomial.

  5. x10 + y3 + t50:There are three variable x, y and t, hence, this is not a polynomial in one variable.

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

    1. 2 + x2 + x

    2. 2 - x2 + x3

    3. π2 x2 + x

    4. 2x - 1

    Solution:

    1. 2 + x2 + x: coefficients of x2 = 1

    2. 2 - x2 + x3: coefficients of x2 = -1

    3. π2 x2 + x: coefficients of x2 = π2

    4. 2x - 1: coefficients of x2 = 0

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

    Solution:

    Binomial of degree 35: 4x35+7

    Monomial of degree 100: 3x100

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

    1. 5x3 + 4x2 + 7x

    2. 4 - y2

    3. 5t - 7

    4. 3

    Solution:

    1. 5x3 + 4x2 + 7x : degree 3

    2. 4 - y2 : degree 2

    3. 5t - 7 : degree 1

    4. 3 : degree 0.

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

    1. x2 + x
    1. x - x3
    1. y + y2 +4
    1. 1 + x
    1. t
    1. r2
    1. 7x3

    Solution:

    1. x2 + x: Quadratic Polynomial
    1. x - x3: Cubic Polynomial
    1. y + y2 +4: Quadratic Polynomial
    1. 1 + x: Linear Polynomial
    1. 3t: Linear Polynomial
    1. r2: Quadratic Polynomial
    1. 7x3: Cubic Polynomial