SOLUTION: The function p is a fourth-degree polynomial with x-intercepts 1.5, 3, and 8 and y-intercept -3. If p(x) is positive only on the interval (3, 8), find p(x).

Question 850059: The function p is a fourth-degree polynomial with x-intercepts 1.5, 3, and 8 and y-intercept -3. If p(x) is positive only on the interval (3, 8), find p(x).
Answer by josgarithmetic(39621) (Show Source): You can put this solution on YOUR website!
REMOVED.
I had solved this but now disagree with my solution.

I would really need to fully re-solve this, but the actual equation in factored form will be .

Second solution, unrefined, was that either one of the factors were repeated or that a new unknown factor x-d would be needed. This was because degree four polynomial function must have four binomial factors, or in some way have a x^4 term when in general form.

I had tried , and solved for d; but the resulting did not work for the interval requirement. Neither did the opposite, .

Testing for a repeated binomial factor, found was exactly one interval over which the function were above or below the x-axis while all the other intervals were the opposite. I then picked the sign necessary to let the y-intercept be -3. The function shown at the top of this solution post was the one that worked.
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