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Math Help - Polynomials Division

  1. #1
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    Polynomials Division

    Hello,

    I'm taking Algebra II (Saxon), and am completely stuck when it comes to dividing polynomials. I don't know how many times I've read the chapter in the textbook over and over again, trying to somehow figure out what I'm supposed to do.. but I just can't seem to get it.

    For example:

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

    Okay, so I write it out like this

    ______________
    x+2) 4x^3 - 3

    Now I'm supposed to mentally change the signs, and add..... I'm stuck already. I completely cannot see the connection between the example in the book, and the explanation it gives me.

    Could anybody explain this to me?? I would REALLY appreciate it.. I need to finish this stuff tonight..
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  2. #2
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    Quote Originally Posted by beckers99 View Post
    Hello,

    I'm taking Algebra II (Saxon), and am completely stuck when it comes to dividing polynomials. I don't know how many times I've read the chapter in the textbook over and over again, trying to somehow figure out what I'm supposed to do.. but I just can't seem to get it.

    For example:

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

    Okay, so I write it out like this

    ______________
    x+2) 4x^3 - 3

    Now I'm supposed to mentally change the signs, and add..... I'm stuck already. I completely cannot see the connection between the example in the book, and the explanation it gives me.

    Could anybody explain this to me?? I would REALLY appreciate it.. I need to finish this stuff tonight..
    The process is very similar to a long division problem with numbers. Think of this as being similar to \frac{4003}{12}.

    Rewrite your first step as:
    Code:
        ______________________
    x+2| 4x^3 + 0x^2 + 0x - 3
    Now, how many times does x (the first term of "x+2") go into 4x^3? 4x^2 times:
    Code:
         __4x^2________________
     x+2| 4x^3 + 0x^2 + 0x - 3
    Now multiply x+2 by 4x^2 and write it in the space below the polynomial:
    Code:
          _4x^2________________
      x+2| 4x^3 + 0x^2 + 0x - 3
           4x^3 + 8x^2
    Now subtract the two lines:
    Code:
          __4x^2________________
       x+2| 4x^3 + 0x^2 + 0x - 3
           -4x^3 - 8x^2
                  -8x^2
    Now bring down the 0x:
    Code:
           __4x^2________________
        x+2| 4x^3 + 0x^2 + 0x - 3
            -4x^3 - 8x^2
                   -8x^2 + 0x
    How many times does x go into -8x^2? -8x times:
    Code:
            __4x^2 - 8x____________
         x+2| 4x^3 + 0x^2 + 0x - 3
             -4x^3 - 8x^2
                    -8x^2 + 0x
    Then:
    Code:
              __4x^2 - 8x__________
          x+2| 4x^3 + 0x^2 + 0x - 3
              -4x^3 - 8x^2
                     -8x^2 + 0x
                     -8x^2 -16x
    Subtract:
    Code:
               __4x^2 - 8x__________
           x+2| 4x^3 + 0x^2 + 0x - 3
               -4x^3 - 8x^2
                      -8x^2 + 0x
                       8x^2 +16x
                             16x - 3
    And again like before:
    Code:
               __4x^2 - 8x + 16______
            x+2| 4x^3 + 0x^2 + 0x - 3
                -4x^3 - 8x^2
                       -8x^2 + 0x
                        8x^2 +16x
                             16x - 3
                            -16x -32
                                 -35
    So \frac{4x^3 - 3}{x+2} = 4x^2 - 8x + 16 - \frac{35}{x + 2}

    -Dan
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  3. #3
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    thank you so much! I think I understand it now!
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