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Math Help - how to do a long division for this cube expression

  1. #1
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    how to do a long division for this cube expression

    (4x^3 + x^2 + 8x + 4) / (x^2 + 2)

    The long division as follows:


    4x
    _______________________
    (4x^3 + x^2 + 8x + 4)
    4x^3 + 8x
    ________
    ??

    Due to truncation of text, the (x^2 + 2) is not shown in the long division diagram.

    The workings:
    4x (x^2 + 2) = 4x^3 + 8x

    I'm stuck with the second step. What about the ^2 exponent?

    The answer key given is 4x + 1 Remainder 2

    Please help. Thanks.
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  2. #2
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    Let me try this:

    For:
    4x (x^2 + 2) = 4x^3 + 8x

    Is it ok to append a zero to get the answer?

    As follows:

    4x^3 + x^2 + 8x + 4
    4x^3 + 0 + 8x
    __________________
    x^2 + 4

    Next Step:

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

    x^2 + 4
    x^2 + 2
    _______
    2

    This approach of adding a zero to the long division allows me to get 4x+1 remainder 2. Is that right?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by shenton View Post
    Let me try this:

    For:
    4x (x^2 + 2) = 4x^3 + 8x

    Is it ok to append a zero to get the answer?

    As follows:

    4x^3 + x^2 + 8x + 4
    4x^3 + 0 + 8x
    __________________
    x^2 + 4

    Next Step:

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

    x^2 + 4
    x^2 + 2
    _______
    2

    This approach of adding a zero to the long division allows me to get 4x+1 remainder 2. Is that right?

    Looks OK to me. You could of course check that

    4x^3 + x^2 + 8x + 4= (4x+1)(x^2+2)+2

    yourself to confirm that your answer is correct.

    RonL
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  4. #4
    Super Member

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    Lexington, MA (USA)
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    Hello, shenton!

    Let me give it a try . . .


    (4x + x + 8x + 4) (x + 2)
    Code:
                     4x    +   1
             --------------------
      x + 2 ) 4x + x + 8x + 4
               4x   +    8x
              ---------------
                     x   +    4
                     x   +    2
                    -------------
                               2
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  5. #5
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    Thanks, Soroban for showing the workings.
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