CHING WAI 發問於 科學及數學數學 · 1 十年前

dividing polynomials 2 --------urgent

1. (a^4 +a^2b^2 +b^4 ) / (a^2 + ab +b^2 ) (152b)<---no need to care about this

2. (2a^3 +a^2 - 5a +2) / (a+1) (153b)

3. (x^2 -3xy +2y^2 +3x - 6y -8) / (x-y+4) (153b)

4. divide x^3 +4x^2 - 5x+3 by x-2 (154a)

5. using the result of (4), write the relatioship between x^3 + 4x^2 -5x +3 and x-2 (154a)

( Ans. x^3 +4x^2 -5x +3 = ?????????????? )

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  • 1 十年前
    最愛解答

    1. (a^4 +a^2b^2 +b^4 ) / (a^2 + ab +b^2 )

    a^2 -ab + b^2

    a^2+ab+b^2 | a^4 + a^2b^2 + b^4

    a^4 + a^3b+a^2b^2

    - a^3b + b^4

    - a^3b - a^2b^2 - ab^3

    a^2b^2 + ab^3 + b^4

    a^2b^2 + ab^3 + b^4

    So, the answer is (a^2 - ab + b^2)

    2. (2a^3 +a^2 - 5a +2) / (a+1)

    If the dividing is a+1 , it will not complete to divided.

    So, it may be dividing a-1

    2a^2 - a - 4

    a + 1 | 2a^3 + a^2 -5a + 2

    2a^3 + 2a^2

    - a^2 - 5a + 2

    - a^2 - a

    - 4a + 2

    - 4a - 4

    6

    2a^2 + 3a - 2

    a - 1 | 2a^3 + a^2 -5a + 2

    2a^3 + 2a^2

    3a^2 - 5a + 2

    3a^2 - 3a

    - 2a + 2

    - 2a + 2

    So the answer will be (2a^2 - a - 4) and remind 6

    or (2a^2 + 3a -2)

    3. (x^2 -3xy +2y^2 +3x - 6y -8) / (x-y+4)

    x - 2y - 1

    x - y + 4 | x^2 - 3xy + 2y^2 + 3x - 6y - 8

    x^2 - xy + 4x

    - 2xy + 2y^2 -x -6y -8

    - 2xy + 2y^2 - 8y

    -x + 2y - 8

    -x + y - 4

    y - 4

    So the answer is (x-2y-1) and remind (y-4)

    4. divide x^3 +4x^2 - 5x+3 by x-2

    x^2 + 6x + 7

    x - 2 | x^3 + 4x^2 - 5x + 3

    x^3 - 2x^2

    6x^2 - 5x + 3

    6x^2 -12x

    7x + 3

    7x - 14

    17

    so the answer is (x^2 +6x + 7 ) and remind 17

    5. using the result of (4), write the relatioship between x^3 + 4x^2 -5x +3 and x-2

    x^3 +4x^2 -5x +3 = (x - 2)(x^2 +6x + 7 ) + 17

    資料來源: Me
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