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Math Help - A general case of polynomial long division?

  1. #1
    Member mfetch22's Avatar
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    A general case of polynomial long division?

    I can't remember how to do polynomial long division (I know, its easy, I shouldn't have forgetten) and I'm having trouble understanding the online explainiations. Can somebody take me through the steps of how to divide: (x-a)^2 into x^4 - 4a^3x+3a^4? So if we let:

    f(x) = x^4 - 4a^3x+3a^4

    and

    h(x) = (x-a)^2 = (x-a)(x-a) = x^2 - 2ax +a^2

    Can somebody show me how to use polynomial long division on:

    g(x) = \frac{x^4 - 4a^3x+3a^4}{(x-a)^2} = \frac{x^4 - 4a^3x+3a^4}{(x-a)(x-a)} = \frac{x^4 - 4a^3x+3a^4}{x^2-2ax+a^2}

    ??

    Thanks in advance
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    You have done the right thing by expanding the demoninator in g(x).

    Long division is pretty tricky in Latex so I suggest read this.

    Polynomial Long Division
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  3. #3
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    Hello, mfetch22!

    I'll give it a try . . .


    (x^4 - 4a^3x+3a^4) \div (x-a)^2


    \begin{array}{cccccccccccc}<br />
&&&&&& x^2 & + & 2ax & + & 3a^2 \\<br />
&& --&--&--&--&--&--&--&-- &--\\<br />
x^2-2ax + a^2 & | & x^4&&&&& - & 4a^3x &-& 3a^4 \\<br />
&& x^4 & - & 2ax^3 & + & a^2x^2 \\<br />
&& --&--&--&--&-- \\<br />
&&&& 2ax^3 &-& a^2x^2 &-& 4a^3x \\<br />
&&&& 2ax^3 &-& 4a^2x^2 &+& 2a^3x \\<br />
&&&& --&--&--&--&-- \\<br />
&&&&&& 3a^2x^2 &-& 6a^3x &+& 3a^4 \\<br />
&&&&&& 3a^2x^2 &-& 6a^3x &+& 3a^4 \\<br />
&&&&&& --&--&--&--&--<br />
\end{array}

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