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HCF x LCM = product of the two polynomials

This type of question, asked 7 times: CDS 1 2017, CDS 2 2017, CDS 2 2018, CDS 2 2020, CDS 2 2022, CDS 1 2026, CDS 2 2026. All 7 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    42
    The HCF of two expressions pp and qq is 1. What is the reciprocal of their LCM ?

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  2. Question 2

    CDS 2 2017

    8
    The product of two non-zero expressions is (x+y+z)p3(x + y + z) p^3. If their HCF is p2p^2, then their LCM is

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  3. Question 3

    CDS 2 2018

    8
    HCF and LCM of two polynomials are (x + 3) and (x3−9x2−x+105)(x^3 - 9x^2 - x + 105) respectively. If one of the two polynomials is x2−4x−21x^2 - 4x - 21, then the other is

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  4. Question 4

    CDS 2 2020

    32
    The HCF and the LCM of two polynomials are 3x+13x + 1 and 30x3+7x2−10x−330x^3 + 7x^2 - 10x - 3 respectively. If one polynomial is 6x2+5x+16x^2 + 5x + 1, then what is the other polynomial ?

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  5. Question 5

    CDS 2 2022

    26
    Let p(x)=x4+x2+1p(x) = x^4 + x^2 + 1, q(x)=x4−2x3+3x2−2x+1q(x) = x^4 - 2x^3 + 3x^2 - 2x + 1. If GCD of p(x)p(x) and q(x)q(x) is x2−x+1x^2 - x + 1, then what is their LCM ?

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  6. Question 6

    CDS 1 2026

    7
    The LCM and HCF of two polynomials p(x) and q(x) are (x+a)(x3−a3)(x + a)(x^3 - a^3) and (x2−ax+a2)(x^2 - ax + a^2), respectively. If p(x)=x4+a2x2+a4p(x) = x^4 + a^2x^2 + a^4, then what is q(x) equal to ?

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  7. Question 7

    CDS 2 2026

    20
    The LCM and HCF of two polynomials p(x)p(x) and q(x)q(x) are (x+k)2(x2−7x+6)(x + k)^2 (x^2 - 7x + 6) and (x+k)(x + k) respectively. If [x3+(2k−1)x2+k(k−2)x−k2][x^3 + (2k - 1)x^2 + k(k - 2)x - k^2] is one of the polynomials, then which of the following statements is/are correct ? I. The other polynomial is (x+k)(x−6)(x + k)(x - 6) where k≠−6k \ne -6. II. (x+k)(x + k) cannot be the HCF if k=−6k = -6. Select the answer using the code given below :

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