Factoring Program

I've written a program that can help a lot with factoring trinomials. I wrote it in C++ first, but then I ported it to TIBasic for graphing calculators. The windows exe version of this program can be found here, the C++ source is here, and the TI verson is here. Of course, that file is only useful if you have a link cable to connect your computer to your calculator. If you don't, talk to me during the day and I'll give you the program. Both the computer and the calculator version pause after their finished. To continue, hit enter. The calculator version also pauses after the screen is filled up so that you'll have time to check the displayed factors. Anyway, it's pretty simple. There are basically eight different types of quadratic trinomial patterns. There's 1++ (ex. x^2+6x+5), 1+-, 1-+, and 1--. Then there's a++ (ex. 5x^2+10x+5), a+-, a-+, and a-- (where a!=1). I'm going to explain how to use my program for each type of pattern. For 1++, 1--, and 1+- patterns, type the value of c (ax^2+bx+c=y) when the program says "c=?" or "number: ". Then match b with the number in the parentheses. The two numbers on either side of the colon are your factors. For example, let's assume you have x^2+20x+36. You would enter 36 for c. The computer (or calculator) would then print:
1:36(37)
2:18(20)
3:12(15)
4:9(13)
6:6(12)
9:4(13)
12:3(15)
18:2(20)
36:1(37)
You would see that the second factor - 2:18(20) - matches b. So your answer is (x+2)(x+18). 1-+ patterns are a tad more complex. For 1-+ patterns, enter c as usual. However, take the opposites of both of your factors and the number in the parentheses. For an example, let's use x^2-13x+36. The calculator gives you the same as above. However, knowing what you know, you invert each of the numbers:
-1:-36(-37)
-2:-18(-20)
-3:-12(-15)
-4:-9(-13)
-6:-6(-12)
-9:-4(-13)
-12:-3(-15)
-18:-2(-20)
-36:-1(-37)
Thus, you'll see that the factors are (x-4)(x-9) because -13=b. Now you're wondering why I even bothered to make this program. After all, 1** patterns are really easy to do in your head. The usefulness of this comes when you're doing a** patterns. For a** patterns, enter c*a for "c=?" or "number: ". Then take the factors and divide the divisible factor by a. More often than not, that will get you the correct answer. However, it is also possible that you'll need to divide both sides by factors of a. For example, 2x^2-11x+15. Enter the number 30 and take the opposites (because the is a -+ pattern) and you'll get:
-1:-30(-31)
-2:-15(-17)
-3:-10(-13)
-5:-6(-11)
-6:-5(-11)
-10:-3(-13)
-15:-2(-17)
-30:-1(-31)
As you can see, the fourth factor is the correct answer, since -11=b. Since you know that -5 is not divisible by 2, you can tell that your factors will be (2x-5)(x-6). Not too complex once you get used to it. Wow, that explanation sucked. If anyone would care to rewrite it in a comment, please go ahead.