College Algebra

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solve the Polynomial inequality and express the solution in set notation.

(3p-2p^2)/(4-p^2)<(3+p)/(2-p)

  • College Algebra -

    You want

    (3p-2p^2)/(4-p^2) - (3+p)/(2-p) < 0

    p(3-2p)/(2-p)(2+p) - (3+p)(2+p)/(2-p)(2+p) < 0

    [p(3-2p) - (3+p)(2+p)]/(2-p)(2+p) < 0

    (3p - 2p^2 - p^2 - 5p - 6)/(2-p)(2+p) < 0

    (3p^2 + 2p + 6)/(2-p)(2+p) > 0

    The numerator is always positive.
    So, we want the region where 4-p^2 is positive.

    That is, -2 < p < 2

    Just to check, graph the two functions, and you'll see that this is the case.

  • College Algebra -

    Factor the polynomials by pulling out the GCF

    6r^2+12r-15

  • College Algebra -

    Sorry, I posted in the wrong place :(

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