Question 1129726
at what  time is your roller coaster at ground level with a polynomial value of x^5-4x^4-7x^3+14x^2-44x+120 and also the breakdown to the exact value of the roots
<pre>Using the RATIONAL ROOT THEOREM, find 2 zeroes. I found 2 zeroes to be 2 and - 3, which results in the 2 factors, (x - 2) and (x + 3). 
FOILing that gives you a trinomial that can be used as the DIVISOR, and with the LONG-DIVISION-of-POLYNOMIALS method, you get yet another trinomial ({{{x^3 - 5x^2 + 4x - 20}}}). 
Using the RATIONAL ROOT THEOREM again will result in a factor (x - 5), and along with LONG-DIVISION-of-POLYNOMIALS method, will result in a binomial ({{{x^2 + 4}}}), which
cannot be factored further.
We now get: {{{highlight_green(matrix(1,7, x^5 - 4x^4 - 7x^3 + 14x^2 - 44x + 120, "=", 0, "======>", (x - 2)(x + 3)(x - 5)(x^2 + 4), "=", 0))}}}
Do you think you can continue from here?
OR
After finding ALL zeroes (there're 3 of them), use each and synthetic division to find the fourth and final factor, and from that, the final zero/solution.