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Math Help - quotient of polynomial

  1. #1
    rcs
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    quotient of polynomial

    when ax^ - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient?
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    Re: quotient of polynomial

    The exponent of x in the first term is missing but here is the general procedure.

    We have ax^\alpha - 4x + 4 = P(x)(x-2)+4, where P(x) is a polynomial of degree \alpha-1
    \implies (ax^\alpha - 4x + 4) - 4 = P(x)(x-2) \implies ax^\alpha - 4x = P(x)(x-2) \implies 2 is a root of ax^\alpha - 4x \implies a2^\alpha = 8 \implies a = \frac{8}{2^\alpha}
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    rcs
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    Re: quotient of polynomial

    when ax^2 - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient? sorry this should have been the correct one...
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    Re: quotient of polynomial

    Quote Originally Posted by rcs View Post
    when ax^2 - 4x + 4 is divided by x - 2, the remainder is 4, what is the quotient? sorry this should have been the correct one...
    perform synthetic division
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    Re: quotient of polynomial

    it is impossible because the numerical coefficient in first term is variable a
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    Re: quotient of polynomial

    Quote Originally Posted by rcs View Post
    it is impossible because the numerical coefficient in first term is variable a
    is that so?

    Code:
    2]   a ..... -4 ...... 4
    .............2a ....(4a-8)
    --------------------------
    .....a....(2a-4) ...(4a-4)
    4a-4 is the remainder ... set that equal to 4 and solve for a


    ... note you could also use the remainder theorem to answer this question.
    Last edited by skeeter; September 9th 2012 at 06:37 AM.
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