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[Powder Miner]

Hello! Have a question about factoring. Well... several, actually. Homework I'm doing, and I feel completely lost, specifically finishing up an earlier worksheet AND doing a new one.
First off! I use a box method of factoring, but this falls short with polynomials difficult to factor.
Example: 5X² - 17x + 6
On the second sheet, there are some polynomials in irregular forms I'm not sure how to change into a more regular form.
Example: 15a²b - 10ab²
(this one is supposed to be factored completely, not even sure about the first...)

[Pnx]

Is that first one supposed to be X to the S? Or is it supposed to have a number in there?

[Powder Miner]

That's supposed to be a 2... I must be tired.

[Vector]

Quadratic formula, babe =]

[Powder Miner]

Aw, man. The quadratic formula is pretty much my nemesis in algebra.
Which is probably why it hadn't come to mind.
It looks to be working now though. Thanks!

[Vector]

It is your friend.  Use it until you love it.

Like, seriously, it is one of the best things ever.  It is your friend.  It loves you back and will be faithful for the rest of your life :I

[Powder Miner]

Ahaha, I can see that.
Back in my algebra and algebra 2 classes, I hadn't got a complete understanding of what I was actually supposed to DO with it.
So I was all like... WHAT DO THESE NUMBERS MEAN?!
The internet solved that mighty fast though.

[Pnx]

Aw, man. The quadratic formula is pretty much my nemesis in algebra.

You're probably going to need it a lot for this course, your teacher may allow you to have it written down on a note card or something, otherwise you might want to make sure you have it memorised.

15a²b - 10ab²

For this one you first want to make sure you factor out the greatest common factor. To find it I find it can help to change it to individual terms being multiplied, so something like this:
15*a*a*b - 10*a*b*b

So we see that both terms have "a" and a "b" that can be taken out of both of them. Both the 15 and the 10 are divisible by 5 so we can also take out 5 from both of them, giving us a factor "5ab", which gives us:

5ab(3a - 2b)
(If you're having trouble wrapping your head around factors, always remember it's just the reverse of multiplying something out)

I think that's all there is to it... I could be wrong.

Ahaha, I can see that.
Back in my algebra and algebra 2 classes, I hadn't got a complete understanding of what I was actually supposed to DO with it.
So I was all like... WHAT DO THESE NUMBERS MEAN?!
The internet solved that mighty fast though.

Your teacher really should have explained this... I mean it's supposed to help you factor a quadratic equation that's hard to factor...

[Powder Miner]

Algebra 1 I had absences smack in the middle of the quadratic formula, my Algebra 2 teacher was just apathetic (my least favorite kind of teacher).
Edit: Haha! Finished the first sheet! ...Now to do the second. All 26 problems... this is going to be one of those nights.
hmm... I'm asked to factor completely for that question you talked about, Pnx. Pretty sure this means that I have to find X a or b or whatever.

[Gamerlord]

Spoiler: Please help me, I can't figure this out! (click to show/hide)

A bank uses Bayes Theorem to help determine whether to give a customer a new credit card. A customer is assessed as either a good credit risk (G) or a bad credit risk (Gc). From historical data the bank has found that 35% of customers considered as a bad credit risk default on their credit card payments. Only 6% of customers considered as a good credit risk default on their payments. Let the symbols G;Gc;D;Dc represent the events of a good credit risk, a bad credit risk, default of payment and not defaulting, respectively.

A new customer applies for a credit card and the bank believes from the initial paper work and checks that there is a 70% chance she is a good credit risk, i.e. Pr(G) = 0:7. After one year the bank has new information as the new customer did not default on any of her payments. Using this new information, nd the probability Pr(GjDc) which is the probability of the customer being a good credit risk given that she didn't default. How does the bank view this customer now?

I'm not sure how to set out the answer OR what they're really looking for...

[Powder Miner]

Yeah, uh, more factoring difficulties. I have a 4th degree polynomial now.
r³+3r²-54r
...How do I factor this?

[Vector]

Factor out the r => quadratic formula.

[Powder Miner]

Aaaand now I feel stupid.
This is what happens when I try to math near midnight.

[Vector]

Don't feel stupid.  I probably have literally a decade of doing this on you.

[Jim Groovester]

The quadratic formula is a pain in the ass to use, especially if you're doing it by hand. It's usually faster and easier to look at the polynomial and see if you can figure out the factors, rather than just immediately going to the quadratic formula.

E.G.:

5x² - 17x + 6

You're looking for factors of 5 that when multiplied with factors of 6 will add up to 17. We know we're looking for a sum and not a difference because the sign of the constant term (the 6 in this instance) is positive. So,

   5 * 3
+ 1 * 2
       17

Now that we know the factors, we just need to ensure that the signs match up. The end result is:

(5x - 2)(x - 3)

r³+3r²-54r

Let's just look at r² + 3r - 54 since that's the important part. Since the sign of the constant term (54) is negative, we're looking for factors of 1 that when multiplied with factors of 54 the result differs by three.

  1 * 6
- 1 * 9
      -3

That we got -3 here is mostly irrelevant since if you change the order you'll end up with +3. The important thing is that the factors differ by 3. Now that we know them, it's just making sure the signs are correct. The result is:

(r + 9)(r - 6)

With the final answer being r(r + 9)(r - 6).

You're probably not practiced enough for this advice to apply to you, but if you're looking at a quadratic and it's not immediately apparent what the factors are, use the quadratic formula. And then if you are practiced enough where this does apply to you, you'll probably plug it into a calculator or a computer. Arithmetic is tedious as hell.