NCERT Class 9 Solutions: Polynomials (Chapter 2) Exercise 2.4 – Part 1

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Q-1 Determine which of the following polynomials has a factor:

Solution:

Understanding relation between polynomial and its roots

Polynomials and Roots

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If is a factor of a polynomial , then we can write, Since zero multiplied by any number is zero. Therefore, this polynomial would become zero for all the values of x where either becomes zero or becomes zero. We don’t know anything about g(x) but we know that becomes zero for . Therefore, Therefore, if x + 1 is a factor of p(x), p(x) must become zero at x = -1. For each polynomial above we would test its value at x = -1. If it comes out to be zero (x+1) is a factor of that polynomial.

  1. Let

Is a factor of polynomial

  1. Let

Is not a factor of polynomial

  1. Let

Is not a factor of polynomial

  1. Let

Is not a factor of polynomial

Q-2 Use the Factor Theorem to determine whether is a factor of in each of the following cases:

Solution:

Zero of is.

If is a factor of then p must also have a zero at -1, i.e.

Is a factor of polynomial.

Zero of is.

If is a factor of then p must also have a zero at -2, i.e.

Is not a factor of polynomial.

Zero of is.

If is a factor of then p must also have a zero at 3, i.e.

Is a factor of polynomial.