Question 148099
I will explain. whenever the {{{x^2}}} term has a coefficient of 1, you start with (x   )(x   ).


in {{{x^2+3x+2}}}, everything is positive, so add two addition signs.

(x+  )(x+  ).


Then, find the factors of 2 that add up to 3.  That would be 2 and 1.  Put them in there.

{{{(x+2)(x+1)}}}. You're done.


In {{{72-22x+x2}}}, first reorder it to {{{x^2-22x+72}}}. Then you start with 

(x   )(x   ).


everything is not positive, only the first and last, so you add two subtraction signs.

(x-  )(x-  ).


Then find the two factors of 72 that would add up to 22. That would be 18 and 4. So put them in there.


{{{(x-4)(x-18)}}}. You're done.


If you want to check them, I would just use the acronym I came up with called SAM.  That stands for Squared, Add, Multiply. And it's easy to remember, especially if your name is Sam.  Anyway, here's how it works:


Start with:
(x+2)(x+1) and (x-4)(x-18)


Then do your SQUARED terms:
(x+2)(x+1) and   (x-4)(x-18)
 {{{x^2}}}     and      {{{x^2}}}


Then ADD your other two numbers (keeping in mind the negatives) and attach the variable:

(x+2)(x+1)  and  (x-4)(x-18)
 {{{x^2+3x}}}    and    {{{x^2-22x}}}


Then MULTIPLY the last two numbers (keeping in mind the negatives):

(x+2)(x+1)  and  (x-4)(x-18)
 {{{x^2+3x+2}}}   and    {{{x^2-22x+72}}}


So now you know how to factor it and how to check your answer!