What's the highest term that goes into 12x³, 8x², and 12x evenly? If it helps, you can break it up into two questions: what's the greatest common factor between 12 and 8, and what's the greatest common factor between x³, x², and x? Once you have those, multiply the two together, and you'll have the greatest common factor for all three monomials.
Also important to keep in mind: when we say we want to "factor" an expression with more than one term added together, what we really want to do is reverse the distributive property. In case you've forgotten, the distributive property is a property of multiplication that states that if you have three numbers a, b, and c, a(b+c) = ab + ac. You distribute the a to each of the terms in the parentheses. Here, you're given the ab + ac part, and you have to work your way back. To give an example, if we had the expression:
[tex]24x+36[/tex]
We can use the fact that 12 is the greatest common factor of 24x and 36 to rewrite it:
[tex]12(2x)+12(3)[/tex]
And, realizing that 12 has been distributed to the 2x and the 3, reverse the distributive property to get:
[tex]12(2x)+12(3)=12(2x+3)[/tex]
