by MrAlgebra on Sun Sep 16, 2012 2:49 pm
When factoring 3x² - 14x + 8, you'll need to find two numbers that multiply to give you ac while adding to give you b. In this case, ac = 3(8) = 24 and b = -14. We'll want to look at negative factors of 24 since we need them to add up to a negative number:
-1 -24, sum = -25 so that's not it
-2 -12, sum = -14 bingo
Now we'll use those two numbers to break up the center term:
3x² - 14x + 8
3x² - 2x - 12x + 8
From here, group the first two terms together and pull out anything you can.
(3x² - 2x) - 12x + 8
x(3x - 2) - 12x + 8
Now do the same thing to the last two terms.
x(3x - 2) - (12x + 8)
x(3x - 2) - 4(3x - 2)
Note that we pulled out -4, so we have to make the last term -2. Now we pull out what we have in the parentheses to get:
x(3x - 2) - 4(3x - 2)
(3x - 2)(x - 4)
You can repeat this process with any trinomial. There are other ways to do it, but this tends to be the most efficient method. Good luck.