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匿名 發問於 科學及數學數學 · 5 年前

Maths Polynomial

When 3x^3 + 8x^2 - 6 is divided by a polynomial , the quotient and the remainder are 3x^2 + 2x - 4 and 2 respectively. Find the polynomial.

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  • 5 年前
    最愛解答

    圖片參考:https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1b...

    When polynomial (A) is divided by polynomial (B), the quotient is polynomial (C) and the remainder is polynomial (D).

    That is, (A) ÷ (B) = (C) ... (D)

    That means, (A) = (B) × (C) + (D)

    That is,

    (Dividend) = (Divisor) × (Quotient) + (Remainder)

    Now,

    (Dividend) = 3x³ + 8x² - 6

    (Quotient) = 3x² + 2x - 4

    (Remainder) = 2

    (Divisor)

    = [ (Dividend) - (Remainder) ] / (Quotient)

    = [ (3x³ + 8x² - 6) - (2) ] / (3x² + 2x - 4)

    = (3x³ + 8x² - 8) / (3x² + 2x - 4)

    = (3x³ + 2x² + 6x² - 8) / (3x² + 2x - 4)

    = (3x³ + 2x² - 4x + 6x² + 4x - 8) / (3x² + 2x - 4)

    = [x(3x² + 2x - 4) + 2(3x² + 2x - 4)] / (3x² + 2x - 4)

    = (x + 2)(3x² + 2x - 4) / (3x² + 2x - 4)

    = x + 2

    {Or you can use long division.}

    圖片參考:https://s.yimg.com/rk/HA00430218/o/868456363.jpg

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