Quadratics of the form x2+bx+c

I am on unit nine, and I'm learning about factorizing quadratic expressions I have actually understood what they are talking about, so today has been a good day for me mathematically speaking.

The process of factorizing these equations are simpler than you may think. basically, the idea of factorizing is to make the equation simpler. for example.

x2+3x+2 can be written in between to pairs or brackets ( )( )
so you need to find a pair of factors that 2 and 3 will have in common.

so if I look at the number 2, well, 1x2=2 and 1+2=3 so there we have our factor pairs.
Factor pairs of 2: 1,2
The pair with the sum 3: 1,2
x2+3x+2=(x+1)(x+2). We can check that this is correct by doing the following.

(check: (x+1)(x+2)=x2+2x+1x+2, now collect the like terms
=x2+3x+2)

so, we know that this factorization is correct as we have got the original equation.