SOLUTION: The problem on my homework says: Find all factors of {{{6x^2+14x-12 }}}. Help please? Thanks.

Question 8427: The problem on my homework says: Find all factors of .
Help please? Thanks.
Answer by drglass(89)   (Show Source): You can put this solution on YOUR website!
There a several ways to solve this. The easiest is to use the quadratic equation, however I suspect, given the results I get from the quadratic equation, that you are actually required to factor the problem, so, how do you do this?

First, notice that you result will have to have the form

.

The goal is to find the values for a, b, c and d. To do this notice that according to the equation,:

ac = 6,
ad + bc = 14 and
bd = -12

There are four possible ways to get ac = 6

a     c     ac
6     1     6
1     6     6
3     2     6
2     3     6
There are twelve ways to get db = -12
d     b     db
12     -1    -12
-12       1   -12
  1   -12     -12
-1     12    -12
6     -2    -12
-6      2    -12
2    -6     -12
-2      6    -12
4     -3    -12
-4      3    -12
3    -4     -12
-3      4    -12

With these numbers, there are forty-eight combinations we can used to find . We could list them, or we try to examine the numbers in these tables. As it happens, 6*3 - 1*4 = 14, which is the result we are looking for. This means, the solution is
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