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Remainders on division by several linear divisors give equations for the coefficients

This type of question, asked 2 times: CDS 1 2018, CDS 2 2019. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2018

    43
    A quadratic polynomial ax2+bx+cax^2 + bx + c is such that when it is divided by xx, (x−1)(x - 1) and (x+1)(x + 1), the remainders are 3, 6 and 4 respectively. What is the value of (a+b)(a + b)?

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  2. Question 2

    CDS 2 2019

    39
    Given that the polynomial (x2+ax+b)(x^2 + ax + b) leaves the same remainder when divided by (x−1)(x - 1) or (x+1)(x + 1). What are the values of a and b respectively ?

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