Question 262783
x^3 + x^2 + 2x + 2

First we look to see if there is a greatest common factor (GCF).  x would have been the GCF, except that the last term doesn't have an x, so that won't work.  There is no GCF, so next we group terms with common factors:
(x^3 + x^2) + (2x + 2)

Then we remove the greatest common factor of each group (and we need to make sure that there will be a common factor after this process)

x^2(x + 1) + 2 (x + 1)  Now we use the distributive property to rewrite the problem:
(x^2 + 2) (x + 1)

The problem is now factored.