Answer
(x+2)(x+1)
Work Step by Step
In order to factor the expression $x^{2}$+3x+2, one will need to find factors of the constant, in this equation 2, that add to the middle coefficient, in this case, 3. Upon deciding the factors, one will need to set up the "shells" (see below) to factor.
1. Two factors that multiply together to get 2, but add to get 3, are the numbers 2 and 1.
2. Each shell will need an x term, and one of the factors decided upon in number 1.
3. (x+1)(x+2)
