CDS 2026 (I) Elementary Mathematics, question 8

Topic: Algebra

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Q8

Which of the following expressions can divide both the polynomials x3+2x2−5x+2x^{3}+2x^{2}-5x+2 and x3+4x2+x−6x^{3}+4x^{2}+x-6 exactly ?

I. x−1x-1

II. x+1x+1

III. x+2x+2

Select the correct answer using the code given below :

  1. (a) I and II only
  2. (b) II and III only
  3. (c) I and III only
  4. (d) I onlyCorrect answer

Solution.

Answer: (d) I only

  1. Apply the factor theorem at 1,−11, - 1 and −2- 2.
  2. At x=1x = 1, both polynomials are zero.
  3. At x=−1x = - 1, the first is 8; at x=−2x = - 2, the first is 12.
  4. Thus neither x+1x + 1 nor x+2x + 2 can divide both.