document.write( "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). \n" ); document.write( "
Algebra.Com's Answer #511938 by josgarithmetic(39623)\"\" \"About 
You can put this solution on YOUR website!
REMOVED.
\n" ); document.write( "I had solved this but now disagree with my solution.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I would really need to fully re-solve this, but the actual equation in factored form will be \"p%28x%29=-%28x-1.5%29%5E2%28x-3%29%28x-8%29\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I had tried \"p%280%29=-3=%28x-1.5%29%5E2%28x-3%29%28x-8%29%28x-d%29\", and solved for d; but the resulting \"d=-%281%2F12%29\" did not work for the interval requirement. Neither did the opposite, \"y=-%28x-1.5%29%5E2%28x-3%29%28x-8%29%28x%2B1%2F12%29\".\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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.
\n" ); document.write( "
\n" );