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Polynomials

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type 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. This one: CDS 2 2026 See all 9 of this type

    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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  2. Question 2

    This type asked 7 times: CDS 1 2017, CDS 2 2017, CDS 2 2018, CDS 2 2020, CDS 2 2022, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 7 of this type

    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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  3. Question 3

    This type asked 7 times: CDS 1 2017, CDS 2 2017, CDS 1 2018, CDS 1 2021, CDS 2 2021, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 7 of this type

    8
    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 :

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  4. Question 4

    This type asked 5 times: CDS 2 2017, CDS 1 2020, CDS 1 2021, CDS 2 2022, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    6
    If (x−5)(x - 5) is the HCF of x2−x−px^2 - x - p and x2−qx−10x^2 - qx - 10, then what is the value of (p+q)(p + q) ?

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  5. Question 5

    This type asked 4 times: CDS 1 2020, CDS 1 2025, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 4 of this type

    3
    If x2−4x+3x^2 - 4x + 3 is a factor of x4+px2+qx^4 + px^2 + q, then what is (p−q)(p - q) equal to ?

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  6. Question 6

    This type asked 4 times: CDS 1 2017, CDS 1 2019, CDS 2 2023, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    18
    What is the LCM of x4+x2y2+y4x^4+x^2y^2+y^4, x3y+y4x^3y+y^4 and x4y2−x3y3x^4y^2-x^3y^3?

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  7. Question 7

    Asked 3 times: CDS 2 2018*, CDS 2 2020*, CDS 1 2026 (* = numbers or wording changed that year) See all 3 times it was asked

    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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  8. Question 8

    This type asked 3 times: CDS 2 2017, CDS 1 2018, CDS 2 2018. This one: CDS 2 2018 See all 3 of this type

    24
    The remainder when 3x3−2x2y−13xy2+10y33x^3 - 2x^2y - 13xy^2 + 10y^3 is divided by (x−2y)(x - 2y) is equal to

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  9. Question 9

    Asked 2 times: CDS 1 2017*, CDS 2 2025 (* = numbers or wording changed that year) See all 2 times it was asked

    9
    (x+2)(x+2) is a factor of which one of the following?

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  10. Question 10

    Asked 2 times: CDS 2 2020, CDS 1 2023 See all 2 times it was asked

    43
    Consider the following statements in respect of the polynomial 1−x−xn+xn+11 - x - x^n + x^{n+1}, where nn is a natural number : 1. It is divisible by 1−2x+x21 - 2x + x^2. 2. It is divisible by 1−xn1 - x^n. Which of the statements given above is/are correct ?

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