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Remainder theorem: remainder, or the number to subtract to make it divisible

This type of question, asked 3 times: 25 Jul 2023 S3, 17 Sep 2024 S3, 19 Sep 2024 S1. All 3 questions below, oldest first.

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  1. Question 1

    25 Jul 2023 S3

    64
    What is the remainder when (x17+1)(x^{17} + 1) is divided by (x+1)(x + 1)?

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  2. Question 2

    17 Sep 2024 S3

    62
    When f(m)=m5+5m4−3m+7f(m) = m^5 + 5m^4 - 3m + 7 is divided by (m−2)(m - 2), then the remainder is _____.

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  3. Question 3

    19 Sep 2024 S1

    63
    What number should be subtracted from x3−4x2−8x+11x^3 - 4x^2 - 8x + 11 to make the number divisible by (x+2)(x + 2)?

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