Pre-Calc

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f(x)=(24x3+68x2+24x−32)/(4x3+56x2+236x+280)

I need help finding the roots and the hole for this problem.

  • Pre-Calc -

    well first of all divide top and bottom by 4
    y=(24x3+68x2+24x−32)/(4x3+56x2+236x+280)
    = (6x^3+17x^2+6 x-8)/(x^3+14x^2+59x+70)

    try factoring the top. I went to an online graphing program and found roots of the top at
    -2 , .5, - 1 1/3
    so try
    (x+2)(2x-1)(3x+4) that works
    now the bottom same way

  • Pre-Calc -

    for the bottom roots are
    -7, -.5 , -2
    so
    (x+7)(2x+1)(x+2)

    well x+2 cancels so we really have
    [ (2x-1)(3x+4) ] / [ (x+7)(2x+1) ]

    that has zeros at 1/2 and -4/3
    and is undefined at -7 and -1/2

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