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Maths 發問於 科學及數學數學 · 5 年前

Polynomial

Let f(x) = x^k + x^k-1 + x^k-2 + ... + x + 1, where k is a constant. When f(x) is divided by x-1, the remainder is 7. Find the remainder when f(x) is divided by x+1.

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  • 5 年前
    最愛解答

    As f(x) = x^k + x^k-1 + x^k-2 + ... + x + 1, therefore, f(1) = 1^k + 1^k-1 + 1^k-2 + ... + 1 + 1==> 7 = k + 1==> k = 6So, f(x) = x^6 + x^5 + x^4 + x^3 + x^2 + x + 1f(-1) = 1 - 1 + 1 - 1 + 1 - 1 + 1 = 1Therefore, when f(x) is divided by x+1, the remainder is 1.

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