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Math Help - Polynomial Quesiton

  1. #1
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    Polynomial Quesiton

    1) When the polynomial 3x^3+ax^2+bx-9 is divided by x-2, the remainder is -5. When it is divided by x+1, the remainder is -16. Determine the values of a and b.

    2) Determine the values of m and n so that the polynomial 2x^3+mx^2+nx-3 and x^3-3mx^2+2nx+4 are both division by x-2.

    Help PLease? and show full solution if you possiblely can...
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  2. #2
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    Quote Originally Posted by Rarrazz View Post
    1) When the polynomial 3x^3+ax^2+bx-9 is divided by x-2, the remainder is -5. When it is divided by x+1, the remainder is -16. Determine the values of a and b.

    P(2) = 3(2)^3+a(2)^2+b(2)-9 = -5

    and

    P(-1) = 3(-1)^3+a(-1)^2+b(-1)-9 = -16

    Can you solve this system?
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  3. #3
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    Quote Originally Posted by pickslides View Post
    P(2) = 3(2)^3+a(2)^2+b(2)-9 = -5

    and

    P(-1) = 3(-1)^3+a(-1)^2+b(-1)-9 = -16

    Can you solve this system?
    huh? yaa i know how to do that,
    but there i are 2 unknown varaible in the equations, a and b
    i just dont know how to get rid one...

    well...

    3(2)^3+a(2)^2+b(2)-9 = -5
    24+2a+2b-9 = -5
    15+2a+2b = -5
    2a+2b = -20
    a+2b = -10
    a+b = -5


    3(-1)^3+a(-1)^2+b(-1)-9 = -16
    -3+a-b-9 = -16
    a-b-12 = -16
    a-b = -4

    now im stuck...
    Last edited by Rarrazz; October 4th 2009 at 04:43 PM.
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  4. #4
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    Quote Originally Posted by Rarrazz View Post


    a+b = -5



    a-b = -4

    now im stuck...

    a+b = -5 ...(1)
     a-b = -4 ...(2)

    (1) - (2) gives

     2b = -1 \Rightarrow b = \dfrac{-1}{2}

    Can you finish it?
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  5. #5
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    Quote Originally Posted by pickslides View Post
    a+b = -5 ...(1)
     a-b = -4 ...(2)

    (1) - (2) gives

     2b = -1 \Rightarrow b = \dfrac{-1}{2}

    Can you finish it?
    sorry, i dont quite understand, can you please explain...
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  6. #6
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    I used these equations from your working above

    a+b = -5 ...(1)
     a-b = -4 ...(2)

    I have labelled them (1) and (2)

    Now saying (1) - (2) cancels out the a

    leaving b-(-b) = 2b

    and -5-(-4) = -1

    making those equal

    2b = -1 \Rightarrow b = \dfrac{-1}{2}

    You can use this to find a.
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  7. #7
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    Quote Originally Posted by pickslides View Post
    I used these equations from your working above

    a+b = -5 ...(1)
     a-b = -4 ...(2)

    I have labelled them (1) and (2)

    Now saying (1) - (2) cancels out the a

    leaving b-(-b) = 2b

    and -5-(-4) = -1

    making those equal

    2b = -1 \Rightarrow b = \dfrac{-1}{2}

    You can use this to find a.
    if you are saying like this,

    P(2) = 3(2)^3 + A(2)^2 - 1/2(2) - 9 = -5

    i tried to figure out a but it is different, the answer from my text book is different...
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  8. #8
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    Quote Originally Posted by Rarrazz View Post
    if you are saying like this,

    P(2) = 3(2)^3 + A(2)^2 - 1/2(2) - 9 = -5
    You should use

    b = \dfrac{-1}{2}

    for

     a+b = -5

     a+\dfrac{-1}{2} = -5

    can you solve for a?
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  9. #9
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    Quote Originally Posted by Rarrazz View Post
    2a+2b = -20
    a+2b = -10
    a+b = -5
    what happened here?

    it is like this

    2a+2b = -20
    2(a+b) = -20
    a+b = -10

    Quote Originally Posted by Rarrazz View Post
    3(2)^3+a(2)^2+b(2)-9 = -5
    24+2a+2b-9 = -5
    somethings gone wrong here aswell

    a(2)^2=4a not 2a
    Last edited by Krahl; October 5th 2009 at 04:04 PM.
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