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sydboe · Mar 21, 2009, 10:24 AM

I need the work too! Numbers in pink are the exponents. Thank you!

Solve a 5th Degree Polynomial to be Graphed:

4x5+8x4-25x3-20x2+51x-18

Curlyben · Mar 21, 2009, 10:54 AM

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galactus · Mar 21, 2009, 11:14 AM

$4x^{5}+8x^{4}-25x^{3}-20x^{2}+51x-18$

By the Rational Root Theorem, the numerator of the zero is a factor of the constant term and the denominator of the root is a factor of the leading coefficient.

So, we look at -18 and 4. The roots will be factors of these.

We know one is a factor. Try it.

Divide x-1 into it and if it reduces to a 4th power you have a root.

$\frac{4x^{5}+8x^{4}-25x^{3}-20x^{2}+51x-18}{x-1}=4x^{4}+12x^{3}-13x^{2}-33x+18$

So, 1 is a root. There's one down and 4 to go.

Then, keep going.

Try dividing x+2 into the fourth power poly you got. If it reduces to a cubic, there's another root.

$\frac{4x^{4}+12x^{3}-13x^{2}-33x+18}{x+2}=4x^{3}+4x^{2}-21x+9$

It reduced to a cubic, therefore, -2 is a root. 3 to go.

And so on.

I got to go now, but I will be back to check on your progress.

Also, you can easily find the roots by just graphing this one. It is a nice one because it has 5 real roots.

Just look at the places where it crosses the x axis. Those are your roots.

If you do not have a calculator, go here and download this free graphing utility that I just used.

http://www.padowan.dk/graph/

sydboe · Mar 22, 2009, 07:17 PM

I found all my zeros but now I'm trying to figure out my max's and minutes and why intercept

galactus · Mar 23, 2009, 10:09 AM

Are you in a calc class?