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Math Help - dividing polynomials, solving for a variable

  1. #1
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    dividing polynomials, solving for a variable

    Question is:

    4x^4 - 15x^2 + px + 6 / 2x+1 gives remainder 2/2x+1 .... Solve for p

    My method in reviewing was to synthetically divide, and begin filling in what I could until p was surrounded, then I told it to put its hand up and surrender... It gave in, and I got the answer of 1.

    But I did a test that had a slightly different question to it, but still a "solve for p" and I did it differently.. In that case, I was given a factor of the polynomial, and so I subbed it in to the equation (when that factor equalled zero) and set it all equal to zero... solved for p.

    I just have a feeling there is a different way I could have done it here in the review...

    Any ideas?
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  2. #2
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    remainder theorem ... if the remainder is 2/(2x+1), then f(-1/2) = 2

    4(-1/2)^4 - 15(-1/2)^2 + p(-1/2) + 6 = 2

    1/4 - 15/4 - p/2 + 6 = 2

    -7/2 + 8/2 = p/2

    1 = p
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