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Thread: product of rational polynomials

  1. #1
    Apr 2009

    product of rational polynomials

    Ok, this is the one that I really need help on. I have tried this several different ways and am not getting the book answer. What is a good strategy for these? Try to factor first? Go ahead and multiply every thing together?
    Any help is appreciated!

    $\displaystyle \frac{9x^2 - 4}{3x^2 - 5x + 2} \cdot \frac{9x^4 - 6x^3 + 4x^2}{27x^4 + 8x}$
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  2. #2
    MHF Contributor red_dog's Avatar
    Jun 2007
    Medgidia, Romania
    $\displaystyle 9x^2-4=(3x-2)(3x+2)$ (use the formula $\displaystyle a^2-b^2=(a-b)(a+b)$)

    $\displaystyle 3x^2-5x+2=(3x-2)(x-1)$

    $\displaystyle 9x^4-6x^3+4x^2=x^2(9x^2-6x+4)$

    $\displaystyle 27x^4+8x=x(3x+2)(9x^2-6x+4)$ (use the formula $\displaystyle a^3+b^3=(a+b)(a^2-ab+b^2)$)
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