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Question 965521: Use FOIL method to solve 6x2−x−2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is 6x^2 - x - 2.
multiply the coefficient of the x^2 term times the constant term to get:
6 * 2 = 12
since the coefficient of your x term is negative and the constant term is negativde, you will be lookking for factors of 12 that subtract from each other to get -1.
factors of 12 are 1*12 and 2*6 and 3*4.
3*4 is the one you are looking for because 3 - 4 = -1 which is the coefficient of the x term.
you now need to break your equation up as follows:
6x^2 - x - 2 becomes:
6x^2 + 3x - 4x - 2
now you need to factor the first 2 terms and the last 2 terms.
associate them using parentheses to get:
(6x^2 + 3x) - (4x + 2)
factor (6x^2 + 3x) to get 3x * (2x + 1)
factor (4x + 2) to get 2 * (x + 1)
your expression becomes:
3x * (2x + 1) - 2 * (2x + 1)
factor out the common term of (2x + 1) to get:
(3x - 2) * (2x + 1)
those are your factors.
now that you have the factors, you can use FOIL to get back to the original equation to see if you did it right.\
(3x - 2) * (2x + 1) is equla to 6x^2 + 3x - 4x - 2 which simplifies to 6x^2 - x - 2 which is the original equation you started with, so you factored well.
factoring is not easy and this was not a simple factoring job.
there are several methods available to factor.
one of them is the box method which is similar to what i just did.
i just didn't use the box.
other methods include the use of the quadratic formula which will always get you an answer.
here's some references for you to look at if you want to learn more about how to factor.
http://www.purplemath.com/modules/factquad.htm
this is a pretty good tutorial and the video is pretty good as well.
factoring quadratics are difficult until you start getting the hang of them.
that only comes through learning how to do it and then practicing.
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