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Math Help - Long division of polynomials

  1. #1
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    Long division of polynomials

    1.)3x^2 + 2x+1 divided by X+2

    2.) 5t-3 divided by t-2

    3.) 6x^4 + 8x^2 -4 divided by 2x+4

    any help is appreciated. Thanks everyone, you ROCK!
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by MathMack View Post
    1.)3x^2 + 2x+1 divided by X+2

    2.) 5t-3 divided by t-2

    3.) 6x^4 + 8x^2 -4 divided by 2x+4

    any help is appreciated. Thanks everyone, you ROCK!
    Hello,
    Code:
      (3x^2 + 2x + 1) / (x + 2) = 3x - 4 + 9/(x+2)
     -(3x^2 + 6x)
    ----------------
             -4x + 1
           -(-4x - 8)
           ------------
                   9
    Code:
       (5t - 3) / (t - 2) = 5 + 7/(t+2)
      -(5t -10)
    -----------
             7
    Code:
       (6x^4 +       8x^2         - 4) / (2x + 4) = 3x^3 - 6x^2 + 16x - 32 + 124/(2x + 4)
     -(6x^4 + 12x^3)
    -------------------
             -12x^3 + 8x^2
           -(-12x^3 - 24x^2)
           --------------------
                       32x^2
                     -(32x^2 + 64x)
                     ------------------
                               -64x - 4
                             -(-64x -128)
                            ---------------
                                     124
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  3. #3
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    Edit: Sorry, didn't see Earboth's much neater post. Please ignore this.

    1. Write the polynomials out as shown and make sure that they are in descending order of the powers.

    2. divide the first term of the dividend by the first term of the divisor and write it above the line as shown.

    3. Multiply this number by the divisor and write it underneath the dividend, keeping the same powers in the same columns

    4. subtract the thingy under the dividend from the dividend.

    5&6. repeat, using the thingy as the new dividend each time until it is a constant.

    Long division of polynomials-longdivide.jpg

    Then you have
    \frac {3x^2+2x+1}{x+2} = 3x-4+\frac {9}{x+2}
    Last edited by badgerigar; December 10th 2007 at 02:06 AM. Reason: didn't see earboth's post
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