PreCalc
posted by Richard on .
f(x)=(24x3+68x2+24x−32)/(4x3+56x2+236x+280)
I need help finding the roots and the hole for this problem.

well first of all divide top and bottom by 4
y=(24x3+68x2+24x−32)/(4x3+56x2+236x+280)
= (6x^3+17x^2+6 x8)/(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)(2x1)(3x+4) that works
now the bottom same way 
for the bottom roots are
7, .5 , 2
so
(x+7)(2x+1)(x+2)
well x+2 cancels so we really have
[ (2x1)(3x+4) ] / [ (x+7)(2x+1) ]
that has zeros at 1/2 and 4/3
and is undefined at 7 and 1/2