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Math Help - polynomials

  1. #1
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    polynomials

    For what value of b will the polynomial
    P(x) = -2x^3+bx^2 -5x +2 have the same remainder when it is divided by x-2 and x + 1?

    I thought of finding the remainder by using the remainder theorm and combine them both, and i thought of foiling it, but that wont work. u can't use divide it since b is still unkown. what do u do!! lol thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lickman View Post
    For what value of b will the polynomial
    P(x) = -2x^3+bx^2 -5x +2 have the same remainder when it is divided by x-2 and x + 1?

    I thought of finding the remainder by using the remainder theorm and combine them both, and i thought of foiling it, but that wont work. u can't use divide it since b is still unkown. what do u do!! lol thanks
    by the remainder theorem, we need P(2) = P(-1)
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  3. #3
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    P(2) = P(-1) , so do u subsititue both of these to x? do u mean that both of these will result in the same remainder?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lickman View Post
    P(2) = P(-1) , so do u subsititue both of these to x? do u mean that both of these will result in the same remainder?
    the remainder theorem says, that if a polynomial P(x) is divided by (x - a) then the remainder is P(a)

    so the remainder when P(x) is divided by x - 2 is P(2) and the remainder when P(x) is divided by x + 1 is P(-1). we want these to be equal, so we set them equal.

    P(2) means you replace all the x's in P(x) with 2 and simplify. do the similar thing for P(-1). set the expressions equal to each other. you will have a linear equation in b, solve for b
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by lickman View Post
    For what value of b will the polynomial
    P(x) = -2x^3+bx^2 -5x +2 have the same remainder when it is divided by x-2 and x + 1?

    I thought of finding the remainder by using the remainder theorm and combine them both, and i thought of foiling it, but that wont work. u can't use divide it since b is still unkown. what do u do!! lol thanks
    You could use synthetic division:

    The synthetic division process for \frac{-2x^3+bx^2-5x+2}{x-2}

    Code:
    __
     2|   -2     b      -5         2
                -4     2b-8      4b-26
         -------------------------------
          -2    b-4    2b-13    |4b-24
    We have a remainder of 4b-24

    Now, the synthetic division process for \frac{-2x^3+bx^2-5x+2}{x+1}

    Code:
    __
    -1|   -2     b      -5         2
                 2     -b-2       b+7
         -------------------------------
          -2    b+2    -b-7      |b+9
    We have a remainder of b+9

    Now, we want a value of b that gives us the same remainder:

    4b-24=b+9\implies 3b=33\implies \color{red}\boxed{b=11}

    I hope this makes sense!

    --Chris
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  6. #6
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    lol hey, thanks for the effort really appreciate but i never learned the synthesis divison lol. so can u use the P(2) = P (-1) and show me haha thanks!?!?!?!
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  7. #7
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    oh nvm, how stupid of me, i understand it thanks! i get it now LOL
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