How to factor trinomials

Question

Hey,
Just out of curiosity, I am trying to make a program that solves trinomials that are in the format of Ax^2 + Bx + C. The user should enter A, B, and C, and will be returned the following output: (Fx + Z) (Dx + X). For those who are familiar with trinomials, it should be fairly simple. For those who are not: Z * X will equal C, and Z + X will equal B, IF D and F are equal to one. If they are not equal to one, the output will be different. It's very hard for me to explain trinomials, but basically multiplying the expression #2 will equal expression #1
EX: Multiply to get 15, add to get -2
x^2 - 2x - 15 = 0
(x + 3) ( x - 5)
EX2:
4x^2 +4x - 3
(2x + 3) ( 2x - 1)
I have gotten up to the point where I can call:
public ArrayList<ArrayList<Integer>> getFactors(int num){
To obtain pairs of factors that I can try to use in the trinomial solver. I don't know how to implement the rest.
My explanation of trinomials is probably quite poor, so please tell me if I'm missing any details
Chris.
EDIT: This is my first attempt at it, but it does not work. It returns all zeroes, meaning that the factors were not found.
    public int[] factorTrinomial(int first, int second, int third){
        ArrayList<ArrayList<Integer>> firstFactors = getFactors(first);
        ArrayList<ArrayList<Integer>> thirdFactors = getFactors(third);
        int[] returnArray = new int[4];
        for(ArrayList<Integer> i: firstFactors){
            for(ArrayList<Integer> x: thirdFactors){
                if((i.get(0) * x.get(1)) + (i.get(1) * x.get(0)) == second){
                    returnArray[0] = i.get(0);
                    returnArray[1] = x.get(0);
                    returnArray[2] = i.get(1);
                    returnArray[3] = x.get(1);
                   //(returnArray[0] + returnArray[1]) ( returnArray[2] + returnArray[3])
        return returnArray;
    }OK, ignore all of the above :) I figured it out. All I need to figure out now is how to factor a negative number...Any ideas please?
Edited by: Chris.Y on Nov 24, 2008 6:02 AM
Edited by: Chris.Y on Nov 24, 2008 6:08 AM

Answer 1

Aah, my bad. I figured it out though, around the moment you posted. Thanks for the reply though :)
Here is the code I used:
    public void displayFactors(ArrayList<ArrayList<Integer>> myList){
        System.out.println("Factors:");
        for(ArrayList<Integer> i: myList){
            for(int x: i){
                System.out.println("    " + x);
    public int[] factorTrinomial(int first, int second, int third){
        ArrayList<ArrayList<Integer>> firstFactors = getFactors(first);
        displayFactors(firstFactors);
        ArrayList<ArrayList<Integer>> thirdFactors = getFactors(third);
        displayFactors(thirdFactors);
        int[] returnArray = new int[4];
        for(ArrayList<Integer> i: firstFactors){
            for(ArrayList<Integer> x: thirdFactors){
                if((i.get(0) * x.get(1)) + (i.get(1) * x.get(0)) == second){
                    returnArray[0] = i.get(0);
                    returnArray[1] = x.get(0);
                    returnArray[2] = i.get(1);
                    returnArray[3] = x.get(1);
                   //(returnArray[0] + returnArray[1]) ( returnArray[2] + returnArray[3])
        return returnArray;
    public ArrayList<ArrayList<Integer>> getFactors(int num){
        ArrayList<Integer> tempArray = new ArrayList<Integer>();
        ArrayList<ArrayList<Integer>> returnArray = new ArrayList<ArrayList<Integer>>();
        if(num > 0){
        for(int i = 1; i <= num; i++){
            if(num % i == 0){
               // if(!(isPresent(returnArray,i) || isPresent(returnArray,num / i)))
                tempArray.add(i);
                tempArray.add(num / i);
            if(tempArray.size() > 0){
            returnArray.add(tempArray); //here adds blanks
            tempArray = new ArrayList<Integer>();
        else if(num < 0){
            //What to do if num < 0
            int absoluteValue = Math.abs(num);
            ArrayList<ArrayList<Integer>> values = getFactors(absoluteValue);
            for(ArrayList<Integer> i: values){
                int tempNum = i.get(0) * -1;
                tempArray.add(tempNum);
                tempArray.add(i.get(1));
                returnArray.add(tempArray);
                tempArray = new ArrayList<Integer>();
        return returnArray;
    }Sorry, I didn't take the time to comment it or format it nicely. But you can get the basic idea.