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Math Help - Polynomial division

  1. #1
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    Polynomial division

    hey guys

    Im fairly sure ive never been taught this and i have a few assignment questions to complete and im struggling to get my head around it.

    The first one is 4x^2 - 3x - 2 divided by 1 - X

    Can anyone give me some tips? hopefully from this first i'll manage the rest

    Thanks
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  2. #2
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    Re: Polynomial division

    This Wikipedia page has a detailed example of long polynomial division. If you just need the remainder, you can use little Bézout's theorem. It says that the remainder when a polynomial f(x) is divided by x-a or a-x is f(a).
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  3. #3
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    Re: Polynomial division

    4x^2-3x-2 is divided by -x+1

    let ax+b be the quotient, then (ax+b)(-x+1)=4x^2-3x-2

    \begin{array}{rr|l}a&b&\times\\\hline-a&-b&-1\\a&b&1\end{array}

    add the results diagonally

    \begin{array}{c}4=-a\\-3=-b+a\\find\ a,\ b\end{array}

    remainder=-2-b
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  4. #4
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    Re: Polynomial division

    Hello, luke11121!

    (4x^2 - 3x - 2) \,\div\,(1 - x)

    The long division should look like this:

    . . \begin{array}{cccccccc} &&& - & 4x & - & 1 \\ && -- & -- & -- & -- & -- \\ -x + 1 & | & 4x^2 & - & 3x & - & 2 \\ && 4x^2 &-& 4x \\ && -- & -- & -- \\ &&&& x & - & 2 \\ &&&& x & - & 1 \\ &&&& -- & --& -- \\ &&&&& - & 1  \end{array}


    4x^2 - 3x + 2 \;=\;(-x+1)(-4x-1) + (-1)
    m . . . . . . . . . . . \text{divisor}\;\;\text{quotient} \;\;\text{remainder}

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  5. #5
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    Re: Polynomial division

    Obviously the problem you have give relates to quadratic function which can have two distinct real roots and multiplying them gives: (x-a)(x-b)=ax^2+bx+c (identity).

    So if you you have been given one of the factors suppose (x-a) is already given:

    Therefore,

    => (x-b)=ax^2/x-b+bx/x-b+c/x-b (where common denominator (x-b) ).

    So its comparabale to arithematic. Compare above identity to below equation:

    if

    x*y=a

    find y

    =>y=a/x

    So thats the idea.

    Hope i helped.
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