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Ray
Lv 6
Ray asked in 科學及數學數學 · 1 decade ago

F4 Maths Dividing Polynomials6

1. Divide the following polynomial.Find Q(x),R(x) No need the steps.

(x^4+2x^3-12x^2-4) / (x^2-2x-6)

2. When A is divided by x^2+x+1, the Q(x) is x^2-2 with R(x) 2x+7. Find the Q(x) and R(x) when A is divided by x^2-2x+4.

1 Answer

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  • wkho28
    Lv 7
    1 decade ago
    Favorite Answer

    1. Divide the following polynomial. Find Q(x), R(x) No need the steps.

    (x^4+2x^3-12x^2-4) / (x^2-2x-6)

        1+4+2

       ------------------------

    1-2-6 ) 1+2-12+0-4

        1-2-6

        --------------

         4-6+0

         4-8-24

        -----------------

          2+24-4

          2 - 4-12

         ---------------

           28+8

    Q(x) = x^2 + 4x + 2

    R(x) = 28x + 8

    2. When A is divided by x^2+x+1, the Q(x) is x^2-2 with R(x) 2x+7. Find the Q(x) and R(x) when A is divided by x^2-2x+4.

    A = (x^2+x+1) Q(x) + R(x)

    = (x^2+x+1)(x^2-2)+2x+7

    = x^4+x^3-x^2-2x-2+2x+7

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

        1+3+1

       ------------------

    1-2+4 ) 1+1-1+0+5

        1-2+4

       --------------

         3-5+0

         3-6+12

        -----------------

          1-12+5

          1 - 2+4

         -----------------

           -10+1

    Q(x) = x^2 + 3x + 1

    R(x) = -10x + 1

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