NCERT Class 9 Solutions: Polynomials (Chapter 2) Exercise 2.4 – Part 2

Q-3 Find the value of k, if Equation is a factor of Equation in each of the following cases:

  1. Equation

  2. Equation

  3. Equation

  4. Equation

Solution:

  • According to factor theorem, if Equation is a factor of Equation , then Equation

  1. Equation

    Equation

    Equation Then,

    Equation

    Equation

    Equation

  2. Equation

    Equation

    Equation Then,

    Equation

    Equation

    Equation

  3. Equation

    Equation

    Equation Then,

    Equation

    Equation

  4. Equation

    Equation

    Equation Then,

    Equation

    Equation

    Equation

Q-4 Factorize:

  1. Equation

  2. Equation

  3. Equation

  4. Equation

FInding the monomial factors of a polynomial

Facttoring a Polynomial Into Monomials

FInding the monomial factors of a polynomial

Solution:

  1. Equation

    Equation

    Equation

    Equation

  2. Equation

    Equation

    Equation

    Equation

  3. Equation

    Equation

    Equation

    Equation

  4. Equation

    Equation

    Equation

    Equation

Q-5 Factorize:

  1. Equation

  2. Equation

  3. Equation

  4. Equation

Solution:

Image describing the factorization of a polynomial.

Finding Factors of a Polynomial

Image describing the factorization of a polynomial.

  1. Equation

    Let us guess a factor Equation and choose value of a arbitrarily as 1.

    Now, putting this value in Equation

    Equation

    So, Equation is a factor of Equation

    Now, Equation

    Equation

    Equation

    Equation

    Equation

    Equation

    So, Equation

  2. Equation

    Let us guess a factor Equation . A should be a factor of 5

    Therefore, Equation

    For Equation

    Equation

    Equation

    Equation

    So, Equation is not a factor of Equation

    For Equation

    Equation

    Equation

    Equation

    So, Equation is a factor of Equation

    Now, Equation

    Equation

    Equation

    Equation

    Equation

    So, Equation

  3. Equation

    Let us guess a factor Equation . A should be a factor of 20

    Therefore, Equation

    For Equation

    Equation

    Equation

    Equation

    So, Equation is not a factor of Equation

    For Equation

    Equation

    Equation

    Equation

    So, Equation is a factor of Equation

    Now, Equation

    Equation

    Equation

    Equation

    Equation

    So, Equation

  4. Equation

    Factors of Equation are Equation

    For Equation

    Equation

    Equation

    Equation

    So, Equation is not a factor of Equation

    Now, Equation

    Equation

    Equation

    Equation

    Equation

    So, Equation

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