# 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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