Posted by **Richard** on Sunday, September 30, 2012 at 9:52am.

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

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

- Pre-Calc -
**Damon**, Sunday, September 30, 2012 at 10:08am
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 -
**Damon**, Sunday, September 30, 2012 at 10:13am
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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