View Full Version : Division: x^3+7x^2+11x+5/x^2+2x+1

sail0r

10-26-2008, 01:59 PM

x^3+7x^2+11x+5/x^2+2x+1

I have done similar problems where the divisor is only two terms, ie x+4 but not with three. How do I do this?

galactus

10-26-2008, 02:26 PM

x^{3}+7x^{2}+11x+\frac{5}{x^{2}}+2x+1

That x^2 in the denominator of the 5/x^2 term creates a fifth degree polynomial. Multiply through by x^2 to eliminate it and you have

a quintic with 5 solutions. 4 complex and 1 real.

It is not too easy to solve because the roots are not nicely behaved. Use tech to do it. That's what I'd do.

galactus

10-26-2008, 02:30 PM

Oh, I just realized, I hope you didn't mean:

\frac{x^{3}+7x^{2}+11x+5}{x^{2}+2x+1}

If that is what you meant, it is not what you posted. That is why grouping symbols are important.

sail0r

10-26-2008, 02:43 PM

:) Whoops that is what I meant

galactus

10-26-2008, 02:50 PM

In that event, try using the rational root theorem on the numerator. Try dividing the top by x+5 and see if it reduces to a quadratic. I bet it will. Then, it will be much easier to finish.

Take note, if you multiply the denominator by x+5, what do you get?. I bet you get the numerator.

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