Math Help - This does not make sense

1. This does not make sense

I have to "Simplify each expression", here is one I have to simplify

-x2 + 8x - 12
-------------
x-2

Please tell me what to do. Also I hate Algebra, it makes me so mad that I have to learn something that I will forget in a few years and will never use it in life, basically the only job you can get by learning algebra is being an algebra teacher

2. Originally Posted by AlgebraIsNeverUsedInLife
I have to "Simplify each expression", here is one I have to simplify

-x2 + 8x - 12
-------------
x-2

Please tell me what to do. Also I hate Algebra, it makes me so mad that I have to learn something that I will forget in a few years and will never use it in life, basically the only job you can get by learning algebra is being an algebra teacher
This is probably not the right place to vent, and I would imagine you are a rather young student of algebra and ignorant of the benefits that a good math foundation can bring you. If you develop a more positive attitude and serious work (study) ethic, you may learn to like it enough to be able to pursue a vocation that involves your knowing a little algebra. Don't close any doors at this point in your life. And what's wrong with being an algebra teacher?

$\frac{-x^2+8x-12}{x-2}$

$\frac{-1(x^2-8x+12)}{x-2}$

$\frac{-1(x-6)(x-2)}{x-2}$

$-(x-6) \ \ or \ \ -x+6 \ \ or \ \ 6-x$

Now, if you don't understand any of the detail given here, someone will be glad to break it down for you. The main thing is not to get discouraged. Hang in there and give it you best effort.

3. thanks for the help and sorry for the rant, and thanks for the encouragement.

now I have another question. where did the -1 come from? that seems to be my main problem with algebra, I can look in an algebra book and see how a problem is done, but they dont tell you why they do the problem that way.

4. Originally Posted by AlgebraIsNeverUsedInLife
thanks for the help and sorry for the rant, and thanks for the encouragement.

now I have another question. where did the -1 come from? that seems to be my main problem with algebra, I can look in an algebra book and see how a problem is done, but they dont tell you why they do the problem that way.
You started out with:

$
\frac{-x^2+8x-12}{x-2}$

Now, by factoring out a -1 in the numerator, it made the trinomial easier to factor. Notice that all the signs changed in the parentheses when the -1 came out.

$
\frac{-1(x^2-8x+12)}{x-2}$

Next, I simply factored the trinomial in the numerator:

$
\frac{-1(x-6)(x-2)}{x-2}$

Then divided out the common factor of $x-2$ and I arrived at the conclusion that you can write in either of the three ways I indicated.