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.



WhatsApp: WhatsApp Now
Email: learn@maxtute.com