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HCF of given polynomials by factorising

This type of question, asked 9 times: CDS 2 2020, CDS 1 2021, CDS 2 2022, CDS 2 2023, CDS 1 2024, CDS 2 2024, CDS 1 2025, CDS 2 2025, CDS 2 2026. All 9 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    31
    What is the HCF of the polynomials x6−3x4+3x2−1x^6 - 3x^4 + 3x^2 - 1 and x3+3x2+3x+1x^3 + 3x^2 + 3x + 1 ?

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  2. Question 2

    CDS 1 2021

    16
    What is the HCF of x3−19x+30x^3 - 19x + 30 and x2−5x+6x^2 - 5x + 6?

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  3. Question 3

    CDS 2 2022

    5
    What is the HCF of (x8−y8)(x^8 - y^8) and (x7−y7+x5y2−x2y5)(x^7 - y^7 + x^5y^2 - x^2y^5) ?

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  4. Question 4

    CDS 2 2023

    19
    What is the HCF of acx3+bcx2+adx2+acdx+bdx+bcdacx^3 + bcx^2 + adx^2 + acdx + bdx + bcd and adx3+acx2+bdx2+bcx+acdx+bcdadx^3 + acx^2 + bdx^2 + bcx + acdx + bcd if HCF (c,d)=1\text{HCF}\,(c, d) = 1, c≠dc \ne d ?

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  5. Question 5

    CDS 1 2024

    23
    What is the HCF of x4−13x2y2−300y4x^4 - 13x^2y^2 - 300y^4, x3−4x2y−4xy2−5y3x^3 - 4x^2y - 4xy^2 - 5y^3 and x3−125y3x^3 - 125y^3 ?

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  6. Question 6

    CDS 2 2024

    37
    What is HCF of a4+2a3+3a2+2a+1a^4 + 2a^3 + 3a^2 + 2a + 1 and a6−2a3+1a^6 - 2a^3 + 1 ?

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  7. Question 7

    CDS 1 2025

    83
    What is the HCF of the polynomials x8+x4+1x^8 + x^4 + 1 and x4+x2+1x^4 + x^2 + 1 ?

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  8. Question 8

    CDS 2 2025

    16
    What is the HCF of x3+y3+3xy−1x^3+y^3+3xy-1 and (x+y)4−1(x+y)^4-1?

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  9. Question 9

    CDS 2 2026

    18
    What is the HCF of x3+x2y−10xy2+8y3x^3 + x^2y - 10xy^2 + 8y^3 and x3+x2y−4xy2−4y3x^3 + x^2y - 4xy^2 - 4y^3 ?

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