Rational Root Theorem says that any rational zeros must be of the form where is an integer factor of the constant term and is an integer factor of the lead coefficient.
For this problem the potential rational roots are:
in this case being 1.
Try 1:
No good, has a remainder
Try -1:
No good.
Try 2:
Ok, 2 is a root. That means is a factor, and from the quotient above we get that is the other factor.
If you don't understand the synthetic division that I demonstrated above, see http://www.purplemath.com/modules/synthdiv.htm for a very good discussion on the subject. By the way, that is an order, not a suggestion.
Now we know that:
Now all you need to do is factor the quadratic trinomial to get the other two factors and calculate the remaining two roots. Hint: 2 times 5 is 10, 2 plus 5 is 7.
