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# Polynomials : Roots, Holes and Vertical Asymptotes

#1:
f(x)=(1x^3-18x^2+101x-168)/(1x^3-2x^2-41x+42)

Find:
All Roots:?
All Holes:?
All Vertical Asymptotes:?

The answer to the 1st question is NOT 8 or -8.

#2:
f(x)= (-2x^3+37x^2-222x+432)/(1x^3+3x^2-64x-192)

I need the roots: (I have two of them (9/2) and (6) but I need the third)?

I need to know the hole (although I have x at 8, however I am missing the y) ?
and the answers can be in decimals or fractions.

#### Solution Preview

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2 questions - within 1 hour please
________________________________________
#1:
f(x)=(1x^3-18x^2+101x-168)/(1x^3-2x^2-41x+42)

Find:

All Roots:?
All Holes:?
All Verical Asymptotes:?

The answer to the 1st question is NOT 8 or -8.

Solution. As x^3-18x^2+101x-168=(x-3)(x-7)(x-8)
and
x^3-2x^2-41x+42=(x-1)(x-7)(x+6)
So,
f(x)=(1x^3-18x^2+101x-168)/(1x^3-2x^2-41x+42)
...

#### Solution Summary

Roots, Holes and Vertical Asymptotes are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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