Question about how to solve: Determine the zeros of f(x) = x4 – x3 + 7x2 – 9x – 18. I am solving this problem using all of the polynomial ways such as decartes rule, fundamental therom and rational root. But it seems when I solve it that way, I either come up one answer short or a completely different answer from what I see everyone else get. How would you solve this and what is the answer?

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RRT says: Rational solutions can only be factors of 18 divided by factors of the coefficient of x^4. Rational roots therefore have the form:\[\pm 18, \pm9, \pm6, \pm3, \pm2, \pm1\]If you try (begin with the simplest, of course, so 1 or -1), you get -1 as a root. You can now write f(x) as (x+1)(x³ ..........). To get the 3rd degree part, you can do a long division or a synthetic division. As soon as you have found it, you can do this trick again: I think 2 is a root as well (just try it), so you can factor out x-2 to get (x+1)(x-2)(x²........). Now you can esily check if there are more rational or even real roots.

Could it be that you are not familiar with synthetic division? It's a real handy trick!

No I know how to do synthetic division, its just after that where everything get messy.

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