Factoring Trinomials???

[timeshifter]

Is there a mathematical way to factor trinomials?

[alkatran]

An extremely complicated one, yes.

Assuming by mathematical you mean "pure equation", like the quadratic formula.

[Jacob Roman]

Boy that is easy.

Let's factor this for example

y² - 5y + 6

1.) Set it up as a product of two to where each will hold two terms.

(     ) (     )

2.) Find the factors that go in the first positions:

(y     ) (y     )

Remember y*y = y²

3.) Find the factors that go in the last positions:

(y -  2) (y -  3)

*-2 and -3 are two numbers whose prod. is 6 
and sum is -5

4.) FOIL to double check if you are correct.

First
Outside
Inside
Last

F + O + I + L

First: 

(y -  2) (y -  3)

(y * y) + O + I + L

Outside:

(y -  2) (y -  3)

(y * y) + (-3 * y) + I + L

Inside:

(y -  2) (y -  3)

(y * y) + (-3 * y) + (-2 * y) + L

Last:

(y -  2)  (y -  3)

(y * y) + (-3 * y) + (-2 * y) + (-3 * -2)

Next we combine like terms:

(y * y) + (-3 * y) + (-2 * y) + (-3 * -2)

y² + -3y + -2y + 6

y² - 5y + 6

It's that easy. Hope this helps.

[timeshifter]

Eh... maybe I should have reiterated a little bit...

I'm a high schooler taking college math courses.. I know how to factor trinomials by hand.

I want to write a calculator program for it, and the thing right now that's proving difficult is factoring each coefficient. If the first term was always 1, it would be a piece of cake. But I'm looking at something like ax²+bx+c where a, b, and c are inequal to 1 or 0. That kinda makes it a bit harder...

I can do it with recursion, but that takes forever. I need an effective and quick factoring system that I can use to set up the rest of the program.

[ralph]

You can try implementing the binomial formula:
http://www.sosmath.com/algebra/factor/fac07/fac07.html