How do you factor a polynomial when one root has been given

So first what you are going to do is divide synthetically your root aka factor into your given equation. Then you are going to kind of guess ands check to find the other factor by synthetically dividing what you have left which should be
x^2 +2x +1 by -5, 5 (to make sure there is no multiplicity), 1, and -1 until you get zero in your remainder spot. The number you used to divide will be your other root.