posted by Tiffany .
factor the polynomials using whatever strategy seems appropriate.
Just by inspection,
How did you get that?
Think of it like factoring
12x^2 - 8x + 1
x^2 - 8x + 12
You want factors of 12 that add to 8
That'd be 6 and 2.
It takes some experience to get quick at factoring by inspection. Do lots of these till you don't have to spend a lot of time guessing.
If the middle term is small, and the last term is negative, you want factors that are close to each other:
(x^2-4x+96) = (x-12)(x+8)
If the middle term is positive, it's easier to imagine factors that add up.
Of course, if you are faced with something like
(12x^2 - 29x + 60)
you will have lots of possible combinations.