Completely factor the trinomial, if possible.

To factor the trinomial , we can first look for a common factor in all the terms.

Notice that each term has at least one in it, so we can factor out :

Next, we need to factor the quadratic . We will use the quadratic formula, where , , and :

Calculating the discriminant:

Now applying the quadratic formula:

Since does not have a perfect square as a factor, we cannot factor the quadratic further over the integers. Thus, the complete factorization of the original trinomial is:

This shows that we have factored out the common term , and the quadratic factor can be left in its current form if we are unable to factor it further with integers.