Factoring Algebraic expressions

[Dman]

Hi,

Need some help with basic factorization of algebraic expressions (in both directions).

Can anyone outline the steps - it's been a while.

Thanks
Dman

[rfernandez]

Dman, we'd love to be helpful but your question is much too broad... entire chapters of math textbooks are devoted to this topic alone. You might be better served by identifying a few problems that you are having trouble with and posting them. (Of course, making sure that the source of the problem is in line with our guidelines.)

Rey

[Guest]

Yes I agree and that's just it, I need help with some of the fundamentals. It's been too long and I'm noticing that more often than others, the mistakes I'm making are not related to the GMAT strategy but more re: my math fundamentals. Thanks for the response. If I get hung up on specifics after my fundamental's review, I will post the equation directly.

[Guest]

Here's one for you - I've always had this difficulty & it turns up often in GMAT Q's.

I can easily simplify an expression like these:

A) (x-3y)(x+y) which equals: x^2 +xy - 3y^2
B) -3x(4x^2 - x + 10) which equals: -12x^3 + 3x^2 - 30x

I just don't have the reflex of spoting them & because of that, not sure how to reverse them back to their simplest or original form.

[StaceyKoprince]

For A, you don't quite have it right. You have to FOIL - multiple First, Outside, Inside, and Last terms:
(x-3y)(x+y)
F: x^2
O: xy
I: -3xy
L: -3y^2

which combines to: x^2 - 2xy - 3y^2

Then, if you want to go the other direction (factor):
First, take a look and see if you can factor anything common from all of the given terms. In this case, we can't.
Then, set up two pairs of parentheses with space between: (.......)(.......) (you don't need the dots - the forum just compresses multiple blank spaces so I had to use them as placeholders!)
Then, split your first term: (x.....)(x.....)
Then decide what your signs should be: two pluses, two minuses, or one of each? To do this:
--look at the sign on the 3y^2 term. It's negative, so I need one of each.
-- If it were positive, I'd need either two pluses or two minuses and I'd look at the sign in front of the xy term to decide.
So now I've got: (x+...)(x-...)
Now place the second variable: (x+...y)(x-....y)
Now ask yourself: what multiples to -3 (the coefficient in front of the final term) and adds to -2 (the coefficient in front of the middle term)? -3 times +1 fits the bill. Place those in the parentheses: (x+1y)(x-3y) or just (x+y)(x-3y)

For your second example, you can actually factor out a common term from all of the given terms: 3x (or -3x, if you want; you can factor out a -1 from anything if you want). For the rest of this one, it doesn't actually work out to integers (or even real numbers), so you wouldn't see anything like that on the test. When they do want you to factor a quadratic, they'll give you something that's easily factorable by hand in 2 minutes - in other words, something that factors to integers.