For the first three, you would have to apply the rational zero theorem ((Broken Link Removed) and then use synthetic division ((Broken Link Removed) to see if the remainder is zero.
For the last two, you would group the terms and factor out a common factor method(http://www.chesapeake.edu/khennayake/MAT113/3.2Solution.htm).
This was done by trial and error assisted by EXCEL. Very tedious!
1.Solution Set: X =-1.5887,0.7772,-1.2089, and 0.8717.
2.X = -2.07316,1.2139,-5.0432, and 2.2307.
3. X = -1.9548,2.1191, and 0.9050.
4. X = -2.218,4.516,-11.908,-1.0917.
5. x^3+x^2 = 15x-15.
x^3+x^2-15x+15 = 0.
NOTE: All values of X shown are called
ZEROES, because they give zero output
when plugged into the Eq.
I hope I've helped.
X = -2.218,1.220,13.923,1.0774.