Math Is Fun Forum

Newman

Member

Registered: 2015-09-21

Posts: 42

Factoring

Yes, I forgot how ridiculous factoring can be. Haha. How crazy does this process get? I understand it takes practice and memorizing identities but does someone have an example and solution for how far it typically goes? I assume there are situations where you could pile on more and more advanced concepts but if anyone has examples, I'd appreciate it. Thanks! How many identities do I have to know? Sheesh. How much time should I expect to spend on this one topic?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

Hi;

Can you factor x^2+5 x+6 ?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

No. I barely understand the question. Haha. I would see that as (x^2+5)(x+6). The only like term I see is the x and wouldn't know how to reconcile the 5 and 6 except with some strange equation that I doubt would be the correct way to go...would love to see the solution.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Unless I should have read that as x^2 + 5x + 6 ??

Last edited by Newman (2015-09-29 07:49:40)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

Hi;

Unless I should have read that as x^2 + 5x + 6 ??

That is the correct way to read it. Have they taught how to factor that?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Oh, u mean (x+2)(x+3)? I know that from that adding and multiplying trick...I think.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

That is correct, so what is the problem?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

I mean, I pretty much grasp (but need to practice) this from math is fun page...just wondering how much farther it goes?
Identities:
a2 - b2      =      (a+b)(a-b)
a2 + 2ab + b2      =      (a+b)(a+b)
a2 - 2ab + b2      =      (a-b)(a-b)
a3 + b3      =      (a+b)(a2-ab+b2)
a3 - b3      =      (a-b)(a2+ab+b2)
a3+3a2b+3ab2+b3      =      (a+b)3
a3-3a2b+3ab2-b3      =      (a-b)3

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

That is about as far as it goes. After that it just takes experience.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Cool. Thanks. I appreciate it.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

Do you have a particular one you need to work on?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

I was briefly looking ahead in a book I'm using to refresh on college algebra and saw some stuff in the section on functions that looked like there might be some weird factoring involved. I'll look again and post one. I'm guessing it probably wasn't factoring now that I think about it but...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

Okay, post it anyway.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Okay, find the rational roots and if possible all roots:

2x^4 - x^3 - 11x^2 + 4x +12 = 0

And: Find y' when y=(x^3 + 3x^2 + 1)(x^2 + 2)

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,432

Website

Re: Factoring

Okay, find the rational roots and if possible all roots:

2x^4 - x^3 - 11x^2 + 4x +12 = 0

Have you heard of the rational root theorem?

And: Find y' when y=(x^3 + 3x^2 + 1)(x^2 + 2)

Might want to either use the product rule or the power rule (after expanding the brackets) here.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Yeah, those two are a little advanced for me. I remember covering the stuff but it's been 20 years and I'm just beginning to relearn algebra. It's actually amazing how much one can remember after that long but the gaps are vast canyons. Haha.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

Yes, use the rational root theorem for the first or Sturm sequences or simply graph it and then use deflation. This is what I did.

Roots of 2x^4 - x^3 - 11x^2 + 4x +12 = 0 are -2, -1, 2, (3 / 2).

The second one can be done without using any calculus at all too but expanding and using the power rule is easiest.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Thanks again guys! Your perspective is more helpful than you might know. The language and approach is very grounding which is why I ask general questions sometimes. Great stuff.

Last edited by Newman (2015-09-29 15:40:07)

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

And going back to this....is this right??
Find y' when y=(x^3 + 3x^2 + 1)(x^2 + 2)

y'= 5x^4 + 12x^3+ 6x^2+ 14x

Thx

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Factoring

Hi;

Correct!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Newman

Member

Registered: 2015-09-21

Posts: 42

Re: Factoring

Yes!! thx