3x^2 + 5x + 2
a = 3 , b = 5 , c = 2
Start by mulitplying a*c = 3 * 2 = 6
Now find two number that multiply to 6 and add up to b or 5
We could use 2 and 3 because ....
3 + 2 = 5
3 * 2 = 6
Now you rewrite....
3x^2 + 3x + 2x + 2
Now pull out common factors...
3x ( x + 1 ) + 2 ( x + 1)
The factors of this expression is ( 3x + 2 ) ( x + 1)