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Thread: Polynomial division

  1. #1
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    Polynomial division

    Question 43 and 44



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    Last edited by topsquark; Jul 12th 2018 at 12:50 PM.
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  2. #2
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    Re: Help #3

    Please show what you have tried. It will be much easier to help you if we know where you are stuck and why. Here is a hint for #43. Show your work for #44 and we can help from there.

    Suppose the function is $f(x)$. Then

    $f(x) = (x+1)p_1(x)$

    $f(x) = (3x-1)p_2(x)+4$

    $f(x) = (3x^2+2x-1)p_3(x) + hx+k$

    Find $f(x)$ when $x+1=0$ and when $3x-1=0$. Then plug that into the third equation and you will get a system of equations that will allow you to solve for $h,k$
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  3. #3
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    Re: Help #3

    Quote Originally Posted by SlipEternal View Post
    Please show what you have tried. It will be much easier to help you if we know where you are stuck and why. Here is a hint for #43. Show your work for #44 and we can help from there.

    Suppose the function is $f(x)$. Then

    $f(x) = (x+1)p_1(x)$

    $f(x) = (3x-1)p_2(x)+4$

    $f(x) = (3x^2+2x-1)p_3(x) + hx+k$

    Find $f(x)$ when $x+1=0$ and when $3x-1=0$. Then plug that into the third equation and you will get a system of equations that will allow you to solve for $h,k$
    When g(x) is divided by x-3 the rem in 3 right,then f(x) is divided by x-3 rem is 57.so what next?should i combine these


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  4. #4
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    Re: Polynomial division

    Write $g(x)+3=(x-3)p(x)$

    Then $g(x)=(x-3)p(x)-3$

    Plug in:

    $f(x)=(x^4-x^3+2x-3)((x-3)p(x)-3)$

    Multiply out.

    $f(x)=(x^4-x^3+2x-3)(x-3)p(x)-3(x^4-x^3+2x-3)$

    The first term is divisible by $x-3$. So use long division on

    $\dfrac{-3x^4+3x^3+0x^2-6x+9}{x-3}$
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