Foo - Math Question! Not homework!

Okay guys I have been starting to review my old math warming myself up for college placement tests and I have run into a problem I can not figure out, nor can my buddy who is about the graduate with a CS degree, -_-. The problem is shown below.

(2x^2-3x-2) / (10+x-3x^2)

It needs to be reduced to the lowest term. I have used my ti-89 to get the answer which is -2x-1/3x , but I just don't know how to get there; and don't and can't rely on my calc for the answer. Some help would be nice, even pointing out a rule or equation I have obviously forgotten.

Hmm, I get (2X+1)/(3X+5)

Top:
2X²-3X-2= (2X+1)(X-2)

Bottom10+x-3X²= -1(3X²-X-10)=(3X+5)(X-2)

(2X+1)(X-2)/(3X+5)(X-2)

(X-2) cancels: Property of One

Result= (2X+1)/(3X+5)

You factor the top and you factor the bottom.

General form of each will be (ax+b)*(cx+d) note any of a b c d may be negative.

D@mn terms escape me right now.

a*c has to equal what you multiply x^2 by. b*d has to equal the simple number involved.

so for (2x^2-3x-2)
a*c = 2 and b*d= 2

so you have (2x ? 2) * (x ? 1) or (2x ? 1) * (x ? 2)
somehow the middle term has to be 3 only way that works is (2x ? 1) * (x ? 2) with 4-1 getting 3.

from there just play with the signs til it fits.

When factoring always check by multiplying it out. That is easy and will catch a lot of silly mistakes.

EDIT:
Of course as soon as I post I remember coeffecient.

This really is easy stuff, but lots of people for some reason go blank as soon as the x squared term has a coeffecient. This is the kind of stuff where practice helps. Remember if it can be factored the coeffecients have to be integers. Also remember if they give one where they are not integers to start multiply (both sides) to get to integers before trying to factor.

Hmm, I get (2X+1)/(3X+5)

Top:
2X²-3X-2= (2X+1)(X-2)

Bottom10+x-3X²= -1(3X²-X-10)=(3X+5)(X-2)

(2X+1)(X-2)/(3X+5)(X-2)

(X-2) cancels: Property of One

Result= (2X+1)/(3X+5)

You forgot your factored out -1.
Im getting (2x-1)/(-3x-5)

If you factor the -1 out of that answer you get something similar to the OP's calculator, just with an additional +5 in the denominator [(-2x+1)/(3x+5)]. Not sure how your calc got that OP.

Edit: To the OP: The easy way to simplify binomials is using the F.O.I.L. method (First, Outer, Inner, Last). An explanation can be found here (http://www.algebrahelp.com/lessons/simplifying/foilmethod) or in any algebra text book.

You forgot your factored out -1.
Im getting (2x-1)/(-3x-5)

If you factor the -1 out of that answer you get something similar to the OP's calculator, just with an additional +5 in the denominator [(-2x+1)/(3x+5)]. Not sure how your calc got that OP.

Edit: To the OP: The easy way to simplify binomials is using the F.O.I.L. method (First, Outer, Inner, Last). An explanation can be found here (http://www.algebrahelp.com/lessons/simplifying/foilmethod) or in any algebra text book.

By gum, I just looked back and I sure did forget I factored out the neg1! Whoops!:D

nor can my buddy who is about the graduate with a CS degree, -_-.

That's too bad as any decent college/uni should've covered this first semester, first year. If not even in highschool.

That's too bad as any decent college/uni should've covered this first semester, first year. If not even in highschool.

They wont get the answer his calc gave him. Im going to guess the OP entered it in incorrectly.

I guess I just missed typing the +5 at the end. Thanks guys, I was trying it a different way. I could have sworn remembering a rule where is you have a negative in either the top or bottom you can switch them to the other. So like x-2/x-3 = x+3/x+2, but I knew that wasn't right and just had a brain fart. 2 months away from a textbook and things aren't coming back fast. Thanks for the help guys.

No worries, I haven't done any factoring all Summer, so I got a tad hazy and forgot the -1 factored out anyway......;)

Thanks, I restart Fall Semester Monday and I'll likely have to do some factoring for n groups anyway for Sociology or Anthropology for statistical studies.

I know what you mean, two months ago I wouldn't had even needed to think about this problem; but algebra has not been a huge focus(not at all actually :D) over the summer so the factor thing just seemed to leave my brain space.