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**Nervous** I don't know about you guys, but I usually have trouble with trinomials such as

$\displaystyle 6x^2+17x+5$

Specifically because I have to use combinations of the factors of 5 and of 6, not to mention the order I use the factors in.

Now, here's my little trick. (And all I can say is that no one ever taught me this in school, I don't know about anyone else, but I come from a pretty uneducated county.)

First, take the factors of the first and last digits, that part is a given.

$\displaystyle Factors of 5, \alpha = {1,5}$

$\displaystyle Factors of 6, \beta = {1, 2, 3, 6}$

Next, find all the products:

$\displaystyle Products of 1 and \beta= {1, 2, 3, 6}$

$\displaystyle Products of 5 and \beta= {5, 10, 15, 30}$

Now, find the two that add to 17:

$\displaystyle 2+15=17$

So, now we know the answer involves {1, 5} and {2, 3}:

The answer turns out to be:

$\displaystyle 6x^2+17x+5=0$

$\displaystyle (2x+5)(3x+1)$

So, did anyone else know this, or am I totally awesome?