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Math Help - divide polyinomial when remainder is given

  1. #1
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    divide polyinomial when remainder is given

    we the polynomial x^4+kx^2-kx+2 by x+2 the remainder is 36. What"s the value of k?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by gumi View Post
    we the polynomial x^4+kx^2-kx+2 by x+2 the remainder is 36. What"s the value of k?
    Synthetically divide and you will get a remainder in terms of k and then you will need to solve f(k)=36
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  3. #3
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    so K= 3

    Is this right?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by gumi View Post
    so K= 3

    Is this right?
    I got k=6....to verify rewrite it assuming k=3 to get f(x)=x^4+3x^2-3x+2 and divide by x+2


    Just to check two common mistakes you did use -2 as your divisor and you did remember to have 5 spaces not four since there is a 0 space for the cubic term?
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  5. #5
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    Hello, gumi!

    We divide the polynomial x^4+kx^2-kx+2 by x+2
    and the remainder is 36. What is the value of k ?
    Are you familiar with the Remainder Theorem?

    Given a polynomial P(x), the remainder when dividing by (x-a) is P(a).


    The remainder when x^4 + kx^2 - kx + 2 is divided by (x + 2) is:

    . . P(\text{-}2) \:=\:(\text{-}2)^4 + k(\text{-}2)^2 - k(\text{-}2) + 2 \:=\:36

    Hence: . 16 + 4k + 2k + 2 \:=\:36\quad\Rightarrow\quad 6k \:=\:18 \quad\Rightarrow\quad\boxed{k \:=\:3}

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