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Product of four linear factors: pair them to get a common quadratic

This type of question, asked 2 times: CDS 2 2017, CDS 1 2021. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2017

    19
    The factors of x(x+2)(x+3)(x+5)−72x (x + 2) (x + 3) (x + 5) - 72 are

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  2. Question 2

    CDS 1 2021

    19
    If x(x−1)(x−2)(x−3)+1=k2x(x - 1)(x - 2)(x - 3) + 1 = k^2, then which one of the following is a possible expression for kk?

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