Answer: (x+1)(x+2)
Step-by-step explanation
This is something to find through trial and error. The idea is to find two numbers that add to 3 and multiply to 2. The two values we want are 1 and 2 since:
1+2 = 3 and 1*2 = 2
So this is how we end up with (x+1)(x+2) as the factorized answer. Use the FOIL rule or distributive property to expand out the answer and you should arrive back at the original polynomial again. This will help confirm the answer. Another way to check the answer is to graph y = x^2+3x+2 and graph y = (x+1)(x+2) to find that both produce the same exact parabola.